diff --git "a/7dFJT4oBgHgl3EQfmywg/content/tmp_files/load_file.txt" "b/7dFJT4oBgHgl3EQfmywg/content/tmp_files/load_file.txt"
new file mode 100644--- /dev/null
+++ "b/7dFJT4oBgHgl3EQfmywg/content/tmp_files/load_file.txt"
@@ -0,0 +1,2314 @@
+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf,len=2313
+page_content='Distributionally Robust Multi-objective Bayesian Optimization under  Uncertain Environments  Yu Inatsu1,∗  Ichiro Takeuchi2,3  1 Department of Computer Science, Nagoya Institute of Technology  2 Department of Mechanical Systems Engineering, Nagoya University  3 RIKEN Center for Advanced Intelligence Project  ∗ E-mail: inatsu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='yu@nitech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='jp  ABSTRACT  In this study, we address the problem of optimizing multi-output black-box functions under uncertain  environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  We formulate this problem as the estimation of the uncertain Pareto-frontier (PF) of a  multi-output Bayesian surrogate model with two types of variables: design variables and environmental  variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  We consider this problem within the context of Bayesian optimization (BO) under uncertain  environments, where the design variables are controllable, whereas the environmental variables are assumed  to be random and not controllable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The challenge of this problem is to robustly estimate the PF when the  distribution of the environmental variables is unknown, that is, to estimate the PF when the environmental  variables are generated from the worst possible distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  We propose a method for solving the BO  problem by appropriately incorporating the uncertainties of the environmental variables and their probability  distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  We demonstrate that the proposed method can find an arbitrarily accurate PF with high  probability in a finite number of iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  We also evaluate the performance of the proposed method  through numerical experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Introduction  In many industrial applications, we encounter the problem of optimizing the multi-output black-box function  under uncertain environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' For example, in the problem of optimizing growing conditions for crops, we want  to optimize several conditions such as fertilizer levels to maximize crop quality and yield under an uncertain  environment such as weather conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  To formulate this problem, let f (1)(x, w) and f (2)(x, w) be a pair of outputs of a black-box function that  we want to simultaneously maximize, where x ∈ X and w ∈ Ω are the design variables (such as fertilizer levels)  and environmental variables (such as weather conditions) defined in domains X and Ω, respectively, where the  former is controllable and the latter is not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' To characterize the uncertainty of the environmental variables w,  we assume that it is sampled from an unknown probability distribution, P †.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Because we do not know P †, we  consider the case where we know only A, which is a family of candidate distributions for w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  This study aims to identify a distributionally robust Pareto-frontier (DR-PF) in the above setting, which is  formulated as a PF of the following two functions:  F (1)(x) =  inf  p(w)∈A  �  Ω  f (1)(x, w)p(w)dw,  F (2)(x) =  inf  p(w)∈A  �  Ω  f (2)(x, w)p(w)dw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Figure 1 shows an example of the problem setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  To identify a DR-PF, it is necessary to predict it and quantify its uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In this study, under the  assumption that f (1)(x, w) and f (2)(x, w) follow a Gaussian process (GP), we developed a Bayesian optimization  (BO) method to find a lower bound of the DR-PF by considering the uncertainty of environmental variables w  and the uncertainty of the probability distribution for w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Specifically, we propose an acquisition function (AF)  that enables us to sequentially select the controllable design variable x in a sample-efficient manner to obtain  the DR-PF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  To this end, various technical challenges need to be resolved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' One difficulty is that, even when f (1)(x, w)  and f (2)(x, w) are GPs, F (1)(x) and F (2)(x) are not GPs anymore.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Therefore, we derive a non-trivial credible  intervals of F (1)(x) and F (2)(x) considering that they are defined as the infima of integrated GPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Furthermore,  although a naive formulation of multi-objective BOs is computationally expensive, the proposed AF has the  advantage that it can be evaluated efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' We also conducted a theoretical analysis of the proposed BO  method to prove that the proposed BO method can find an arbitrarily accurate DR-PF with a high probability  in a finite number of iterations under mild conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Related Work  For black-box function optimization problems, BOs have been popularly used [Settles, 2009, Shahriari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2016]  in which GP [Williams and Rasmussen, 2006] is often employed as a surrogate model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' An optimization problem  1  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='11588v1  [stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='ML]  27 Jan 2023  Multi-objective function  � �, � = � � �, � , � � �, �  (a)  Objective function 1  x  w  4  2  0  2  4  4  2  0  2  4  0  5  10  15  20  25  30  35  40  Objective function 2  x  w  4  2  0  2  4  4  2  0  2  4  0  10  20  30  40  50  60  70  80  (b)  Candidate distributions of  4  2  0  2  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  Candidate distribution of w  w  Density  4  2  0  2  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  Candidate distribution of w  w  Density  4  2  0  2  4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  Candidate distribution of w  w  Density  ・  ・  ・  ・  ・  ・  ・・・  ・  ・  ・・・  ・  ・  ・・・  ・  (c)  Expected value of � � (�,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' �)  Expected value of � � (�,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' �)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Candidate Pareto-frontiers  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Distributionally robust  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Pareto-frontier  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Pareto-frontier  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Figure  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1: Conceptional diagram of a DR-PF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The upper and lower color maps in (a) represent objective  functions f (1)(x, w) and f (2)(x, w), respectively, where x and w are the scalar design and environmental variable,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The plots within the frame in (b) represent multiple candidate distributions for w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' A dashed line  in (c) is the expected PF for each candidate distributions of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' A red solid line is the DR-PF, which is defined  by the worst-case expectation of the candidate distributions, provides a lower bound of uncertain PF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The  objective of this study is to efficiently identify the DR-PF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  of multiple black-box functions is typically formulated as a Pareto optimization problem, and BO methods for  such problems have been also studied [Zuluaga et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2016, Suzuki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Many studies have been conducted on BOs under uncertain environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' For example, [Bogunovic et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2018]  proposed a BO method to maximize the worst-case function value with respect to a shift in the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In several  studies [Beland and Nair, 2017, Toscano-Palmerin and Frazier, 2018, Oliveira et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2019, Fr¨ohlich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2020,  Gessner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2020], a BO problem to maximize the expected value of a black-box function with respect to the  input distribution was considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Furthermore, several studies considered the simultaneous optimization of  multiple black-box functions under the assumption that the distribution of environmental variables is known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  For example, [Iwazaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2021] dealt with constrained optimization and Pareto optimization problems for the  mean and variance of a black-box function with respect to environmental variables, [Qing et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2022] considered  Pareto optimization problems for the expected values of multiple objective functions, and [Amri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2021]  dealt with chance-constrained optimization problems that is an extension of constrained optimization problems  to the input uncertainty setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Distributionally robust optimization (DRO) was first introduced by [Scarf, 1958].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Because DRO is an im-  portant topic in the context of robust optimization and has been the subject of numerous studies, we refer an  exhaustive survey of DRO to [Rahimian and Mehrotra, 2019].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In recent years, several studies on DRO in the  context of BOs (DRO-BOs) have been conducted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' [Kirschner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2020] and [Nguyen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2020] proposed  BO methods to efficiently find the design variable that maximizes F (1)(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' DRO-BOs have also been stud-  ied under multiple black-box functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' [Inatsu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2022] proposed a BO method for distributionally robust  chance-constrained problems, which is an extension of the chance-constrained problem to DRO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' However, to the  best of our knowledge, there are no prior studies on BOs for Pareto optimization under the DRO framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Contributions  The contributions of this study are as follows:  We develop a BO method for identifying DR-PFs called DR-PF BO method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Specifically, we propose a  novel AF for the DR-PF BO, which is computationally inexpensive and has theoretical guarantees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Under mild conditions, we prove that the DR-PF BO method can find an arbitrarily accurate PF with a  high probability in a finite number of iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Additionally, we prove that with a specification of an appropriate family of candidate distributions, even  if the true distribution is unknown, the DR-PF BO method can find an arbitrarily accurate expected PF  on the true distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  2  We confirm the performance of the proposed method through numerical experiments with benchmark  functions and simulator-based functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Preliminaries  Let f (1) : X × Ω → R and f (2) : X × Ω → R be the expensive-to-evaluate black-box functions1, where X  and Ω are the finite sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' For each input (x, w) ∈ X × Ω, the values of f (1)(x, w) and f (2)(x, w) are observed  with observation noise as y(1) = f (1)(x, w) + ε(1) and y(2) = f (2)(x, w) + ε(2), where ε(1) and ε(2) are random  samples from independent normal distributions with the mean zero and variances σ(1)2  noise and σ(2)2  noise, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  In this study, the environmental variable w ∈ Ω was assumed to be a discrete random variable that follows an  unknown probability distribution P †.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The two distinct phases called the development phase and use phase exist  in the literature of BOs under uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In the development phase, environmental variables are completely  controllable as design variables, whereas they are stochastic and uncontrollable in the use phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In this study,  we consider the development phase, and the use phase is described in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Furthermore, we denote the  family of candidate distributions of w as A and consider the following class of distributions:  A = {p(w) | d(p(w), p∗(w)) ��� ξ},  where p∗(w) is a user-specified reference distribution, d(·, ·) is a given distance metric function between dis-  tributions, and ξ ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' This means that we consider a set of candidate distributions whose distance from the  reference distribution is not larger than a certain threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Subsequently, the distributionally robust expecta-  tions F (1)(x) and F (2)(x) for each design variable x ∈ X are defined as follows:  F (1)(x) =  inf  p(w)∈A  �  w∈Ω  f (1)(x, w)p(w),  F (2)(x) =  inf  p(w)∈A  �  w∈Ω  f (2)(x, w)p(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  The objective of this study is to efficiently identify the PF determined by F (1)(x) and F (2)(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Let F (x) =  (F (1)(x), F (2)(x)) for each x ∈ X, and let F (E) = {F (x) | x ∈ E} for a set E ⊂ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Furthermore, for a set  B ⊂ R2, we denote the domain dominated by B and the PF of B, respectively, by  Dom(B) = {y ∈ R2 |∃ y′ ∈ B s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' y ⪯ y′},  Par(B) = ∂(Dom(B)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Here, for a point a = (a1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , am) and b = (b1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , bm), a ⪯ b implies ai ≤ bi for any i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , m}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' For a set  C, ∂(C) denotes the boundary of C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The PF determined by F (1)(x) and F (2)(x) can then be written as  Z∗ = Par(F (X)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Gaussian Process  In this study, we use GP surrogate models for black-box functions f (1) and f (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' First, we assume that  f (1) and f (2) follow GP priors GP(0, k(1)((x, w), (x′, w′))) and GP(0, k(2)((x, w), (x′, w′))), respectively, where  k(1)((x, w), (x′, w′)) and k(2)((x, w), (x′, w′)) are the positive-definite kernels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' For l ∈ {1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' 2},' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' given a dataset  {(xi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' wi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' y(l)  i )}t  i=1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' where t is the number of queried instances,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' the posterior distribution of f (l) is a GP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' and its  posterior mean µ(l)  t (x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w) and posterior variance σ(l)2  t  (x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w) are given by  µ(l)  t (x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w) = k(l)  t (x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w)⊤(K(l)  t  + σ(l)2  noiseIt)−1y(l)  t ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  σ(l)2  t  (x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w) = k(l)((x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w)) − k(l)  t (x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w)⊤(K(l)  t  + σ(l)2  noiseIt)−1k(l)  t (x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  where k(l)  t (x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w) is the t-dimensional vector,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' whose jth element is k(l)((x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (xj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' wj)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' y(l)  t  = (y(l)  1 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , y(l)  t )⊤,  It is the t × t identity matrix, K(l)  t  is the t × t matrix whose (j, k) element is k(l)((xj, wj), (xk, wk)), with a  superscript ⊤ indicating the transpose of vectors or matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Proposed Method  Here, we propose a BO method to efficiently identify Z∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Because the functions f (1)(x, w) and f (2)(x, w)  are random variables following GPs, F (1)(x) and F (2)(x) are also random variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Therefore, a reasonable  approach is to construct credible intervals for F (1)(x) and F (2)(x), and use them to estimate the PF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' However,  1Note that the method proposed in this study can be straightforwardly extended to the case where there are more than three  objective functions f(1), f(2), f(3), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='.  3  unlike f (1)(x, w) and f (2)(x, w), F (1)(x) and F (2)(x) do not follow GPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Therefore, we cannot directly obtain  credible intervals using the properties of GPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1, we construct credible intervals for F (1)(x) and  F (2)(x) using the method proposed by [Kirschner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2020] and provide a method for estimating the PF  based on the constructed credible intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Credible Intervals and PF Estimation  For each input (x, w) ∈ X × Ω and time t, the credible interval of f (1)(x, w) is denoted by Q(f (1))  t  (x, w) =  [l(f (1))  t  (x, w), u(f (1))  t  (x, w)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Here, the lower value l(f (1))  t  (x, w) and the upper value u(f (1))  t  (x, w) are given as  l(f (1))  t  (x, w) = µ(1)  t (x, w) − β1/2  1,t σ(1)  t  (x, w),  u(f (1))  t  (x, w) = µ(1)  t (x, w) + β1/2  1,t σ(1)  t  (x, w),  where β1/2  1,t  ≥ 0 is a user-specified tradeoff parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  We then define the credible interval Q(F (1))  t  (x) ≡  [l(F (1))  t  (x), u(F (1))  t  (x)] of F (1)(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Here, the lower and upper values are respectively given by  l(F (1))  t  (x) =  inf  p(w)∈A  �  w∈Ω  l(f (1))  t  (x, w)p(w),  u(F (1))  t  (x) =  inf  p(w)∈A  �  w∈Ω  u(f (1))  t  (x, w)p(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1)  Notably, if the L1- (or L2-) norm is used as the distance d(·, ·) between the distributions, the problem of  obtaining the lower and upper values in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1) is reduced to a linear programming problem (or a second-order  cone programming problem).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In either case, the existence of a fast solver of these problems enabled us to obtain  Q(F (1))  t  (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Similarly, we define credible intervals Q(f (2))  t  (x, w) = [l(f (2))  t  (x, w), u(f (2))  t  (x, w)] for f (2)(x, w) and  Q(F (2))  t  (x) ≡ [l(F (2))  t  (x), u(F (2))  t  (x)] for F (2)(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Next, for any input x ∈ X and any subset E ⊂ X, we define  LCBt(x), UCBt(x) and LCBt(E) as follows:  LCBt(x) = (l(F (1))  t  (x), l(F (2))  t  (x)),  UCBt(x) = (u(F (1))  t  (x), u(F (2))  t  (x)),  LCBt(E) = {LCBt(x) | x ∈ E}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  The estimated PF solution set ˆΠt ⊂ X for the design variables is then defined as follows:  ˆΠt = {x ∈ X | LCBt(x) ∈ Par(LCBt(X))}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Figure 2 (a) shows a conceptual diagram of LCBt(x) and UCBt(x), and (b) shows a conceptual diagram of  Par(LCBt(X)) and ˆΠt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Acquisition Function  Here, we propose an AF for determining the next evaluation point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' First, for each point a ∈ Rm and subset  B ⊂ Rm, we denote the closeness between them as  dist(a, B) = inf  b∈B d∞(a, b),  where d∞(a, b) denotes the metric function given by d∞(a, b) = max{|a1 − b1|, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , |am − bm|}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Using this, we  define AF at(x) for x ∈ X as  at(x) = dist(UCBt(x), Dom(LCBt(ˆΠt))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  We then select the following evaluation points, as described in the following definition:  Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The next design variable, xt+1, to be evaluated is selected as follows:  xt+1 = argmax  x∈X  at(x),  and the next environmental variable, wt+1, to be evaluated is selected as  wt+1 = argmax  w∈Ω  {σ(1)2  t  (xt+1, w) + σ(2)2  t  (xt+1, w)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  4  𝐹(2)(𝒙)  𝐹(1)(𝒙)  𝐹(2)(𝒙)  𝐹(1)(𝒙)  𝐹(2)(𝒙)  𝐹(1)(𝒙)  (a)  (b)  (c)  𝒙1  𝒙2  𝒙3  𝒙4  𝒙5  𝒙6  𝒙7  Figure 2: Conceptual diagrams of LCBt(x), UCBt(x), Par(LCBt(X)), ˆΠt and AFs for seven input points  x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , x7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' At each point x in the left figure (a), LCBt(x) and UCBt(x) indicate the lower left point and the  upper right point of the dashed rectangular region, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In (b), the PF (red line) computed using each  LCBt(x) is Par(LCBt(X)), and because it is constructed by LCBt(x1), LCBt(x2), LCBt(x3), LCBt(x7), ˆΠt  is given by ˆΠt = {x1, x2, x3, x7}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In (c), the light red region indicates Dom(LCBt(ˆΠt)), the region dominated  by the red points (LCBt(ˆΠt)), and at(x) is the closeness between the light red region and UCBt(x) (purple  point).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The furthest point is represented by the purple triangle, UCBt(x4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Thus, the next design variable to  be evaluated is x4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Figure 2 (c) shows a conceptual diagram of the AF at(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Here, AF at(x) can be computed analytically  using the following lemma:  Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Let UCBt(x) = (u1, u2) and LCBt(ˆΠt) = {(l(i)  1 , l(i)  2 ) | 1 ≤ i ≤ k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, at(x) can be computed  as follows:  ˜at(x) = min  1≤i≤k max{u1 − l(i)  1 , u2 − l(i)  2 },  at(x) = max{˜at(x), 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Notably, when the number of objective functions is m ≥ 3, at(x) is easily extended as follows:  ˜at(x) = min  1≤i≤k′ max{u1 − l(i)  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , um − l(i)  m },  at(x) = max{˜at(x), 0},  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2)  where UCBt(x) = (u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , um) and LCBt(ˆΠt) = {(l(i)  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , l(i)  m ) | 1 ≤ i ≤ k′}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The proofs of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1 and  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2) are presented in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' From Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1, once LCBt(ˆΠt) is computed, the maximum value of at(x)  can be analytically obtained by performing 2|X| times inf calculations and computing u(F (1))  t  (x) and u(F (2))  t  (x)  for all x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' On the other hand, an AF based on exact posterior distributions of target functions such as the  expected hypervolume improvement [Emmerich, 2005] for ordinary Pareto optimization, requires approximation  by sampling from f (1)(x, w) and f (2)(x, w) under this problem setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' However, in each posterior sample, the  inf calculation must be performed again to calculate F (1)(x) and F (2)(x) for all design variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Therefore, if  the number of Monte Carlo samples is M, M times more inf calculations are required compared to the proposed  AF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The comparison of computational times is given in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Stopping Condition  Here, we describe the stopping conditions of the proposed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' 2 (c), AF at(x) represents  the closeness of the pessimistic PF and the optimistic predictive value of F (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  That is, if this value is  sufficiently small, there is little room for improvement in the PF;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' therefore, it is reasonable to use it as the  stopping condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Let ϵ > 0 be a user-specified parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then the algorithm is terminated if at(x) ≤ ϵ is  satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The pseudocode for the proposed algorithm is given in Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Theoretical Analysis  Here, we provide the theorems for the accuracy and convergence of the proposed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The details of  the proofs are presented in Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' First,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' to provide theoretical results,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' we assume that f (1) and f (2) follow  5  Algorithm 1 BO for identifying DR-PF  Input: GP priors GP(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' k(1)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' GP(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' k(2)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' parameter ξ ≥ 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' tradeoff parameters {β1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='t}t≥0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' {β2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='t}t≥0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' stopping  parameter ϵ > 0  t ← 1  while at(x) > ϵ do  Compute Q(F (1))  t  (x) and Q(F (2))  t  (x) for each x ∈ X  Select the next evaluation point (xt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' wt)  Observe y(1)  t  = f (1)(xt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' wt) + ε(1)  t  and y(2)  t  = f (2)(xt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' wt) + ε(2)  t  at the point (xt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' wt)  Update GPs by adding observed points  t ← t + 1  end while  Output: Return ˆΠt as the estimated set of design variables comprising the DR-PF  GPs GP(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' k(1)((x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (x′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w′))) and GP(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' k(2)((x,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (x′,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' w′))),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Moreover, we assume that the  prior variances k(1)((x, w), (x, w)) ≡ σ(1)2  0  (x, w) and k(2)((x, w), (x, w)) ≡ σ(2)2  0  (x, w) satisfy  max  (x,w)∈X×Ω σ(1)2  0  (x, w) ≤ 1,  max  (x,w)∈X×Ω σ(2)2  0  (x, w) ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Furthermore, let κ(1)  T  and κ(2)  T  be the maximum information gains of f (1) and f (2) at time T, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Notably, the maximum information gain is a measure often used in theoretical analyses of GP-based BO (see,  e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', [Srinivas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2010]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Here, for each j ∈ {1, 2}, using the mutual information I(y(j);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' f (j)) between y(j)  and f (j), κ(j)  T  can be expressed as  κ(j)  T  =  max  A⊂X×Ω I(y(j)  A ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' f (j)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Next, to quantify the goodness of the predicted ˆΠt, we define an ϵ-accurate Pareto region Zϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' With user-specified  positive numbers ϵ and ϵ = (ϵ, ϵ), we define Zϵ as  Zϵ = {y ∈ R2 |∃ y′ ∈ Z∗ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' y ⪯ y′ and ∃y′′ ∈ Z∗ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' y′′ ⪯ y + ϵ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  That is, Zϵ is the set of points that lie inside Z∗ and within ϵ in the sense of d∞(·, ·)-distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The concept of  Zϵ was also used in [Zuluaga et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2016].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Using Zϵ, we define the accuracy of ˆΠt in terms of the following two  aspects:  Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1 (Accuracy for ˆΠt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Let ϵ be a positive value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' We then define ˆΠt as an ϵ-accurate estimated  solution set if the following holds:  F (ˆΠt) ⊂ Zϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1)  Moreover, we define ˆΠt as an ϵ-accurate estimated Pareto solution set if the following holds:  Par(F (ˆΠt)) ⊂ Zϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2)  It is easy to obtain a set that satisfies either (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1) or (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Generally, by ignoring F (2)(x) and focusing  only on the maximization of F (1)(x), the maximization point x∗ can be estimated using methods such as  [Kirschner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Subsequently, by letting ˆΠt = {x∗}, (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1) is satisfied with high probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Similarly,  if we predict that all points constitute the PF, that is, ˆΠt = X, then (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2) is satisfied because Par(F (ˆΠt)) =  Par(F (X)) = Z∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The following theorem guarantees that the proposed algorithm satisfies both (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2)  with a high probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Let t ≥ 1 and δ ∈ (0, 1) and define β1,t = β2,t = 2 log(2|X × Ω|π2t2/(6δ)) ≡ βt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In addition, let  ϵ > 0 be a user-specified stopping parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, when Algorithm 1 terminates, ˆΠt satisfies (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2)  with a probability of at least 1 − δ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1 does not indicate whether the algorithm terminates or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The following theorem guarantees  the convergence of Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Under the same conditions as those in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1, let T be the smallest positive integer that  satisfies the following inequality:  βT (C1κ(1)  T  + C2κ(2)  T )  T  ≤ ϵ2  4 ,  where C1 = 2/ log(1+σ(1)−2  noise ) and C2 = 2/ log(1+σ(2)−2  noise ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, Algorithm 1 terminates after at most T trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Simulator setting  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='iteration  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='R1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Random  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='UCB_F1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='UCB_F2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='MVA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='EHI  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Proposed  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Simulator setting  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='iteration  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='R2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Random  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='UCB_F1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='UCB_F2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='MVA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='EHI  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Proposed  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Uncontrollable setting  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='iteration  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='R1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Random  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='UCB_F1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='UCB_F2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='MVA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='EHI  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Proposed  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Uncontrollable setting  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='iteration  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='R2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='200  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='300  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='400  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Random  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='UCB_F1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='UCB_F2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='MVA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='EHI  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Proposed  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Figure 3: Average values of R1 and R2 for each method in Simulator and Uncontrollable settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The length  of each error bar represents twice the standard error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='SIR (case1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='iteration  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='R1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='10  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='25  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='30  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='35  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Random  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='UCB_F1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='UCB_F2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='MVA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='EHI  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Proposed  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='SIR (case1)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='iteration  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='R2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Random  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='UCB_F1  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='UCB_F2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='MVA  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='EHI  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='Proposed  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='20  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='40  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='60  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='80  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='100  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  SIR (case2)  iteration  R1  0  20  40  60  80  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  0  20  40  60  80  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  0  20  40  60  80  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  0  20  40  60  80  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  0  20  40  60  80  100  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='0  Random  UCB_F1  UCB_F2  MVA  EHI  Proposed  0  20  40  60  80  100  0  10  20  30  40  SIR (case2)  iteration  R2  0  20  40  60  80  100  0  10  20  30  40  0  20  40  60  80  100  0  10  20  30  40  0  20  40  60  80  100  0  10  20  30  40  0  20  40  60  80  100  0  10  20  30  40  0  20  40  60  80  100  0  10  20  30  40  Random  UCB_F1  UCB_F2  MVA  EHI  Proposed  Figure 4: Average values of R1 and R2 for each method in Case1 and Case2 in SIR model experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The  length of each error bar represents twice the standard error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Table 1: Computational time (second) and the ratios of the computational time to that of the proposed method  Random  UCB F1  UCB F2  MVA  EHI  Proposed  Computational time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='068  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='067  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='135  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='21  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='139  (Standard error)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='001)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='011)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='001)  Computational time ratio  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='496  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='488  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='985  118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='68  1  (Standard error)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='004)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='004)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='006)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='548)  (0)  Here, because the maximum information gains κ(1)  T  and κ(2)  T  are known to be sublinear with respect to T  under mild assumptions [Srinivas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2010], and the order of β1,T = β2,T is O(log T), the positive integer T  satisfying the inequality in Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2 exists.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  We emphasize that Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1 also holds in the use phase setting and a similar theorem holds for Theorem  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2 under mild additional conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Moreover, by appropriately designing the family of candidate distributions  using the empirical distribution as the reference distribution, the proposed method provides an arbitrarily  accurate solution for the expected PF based on the true distribution, even when the true distribution is unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Details are provided in Appendix A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Numerical Experiments  Here, we confirm the performance of the proposed method using synthetic functions and real-world simulation  models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In this experiment, we used a one-dimensional design variable x and environmental variable w and the  following Gaussian kernels:  k(1)((x, w), (x′, w′)) = σ2  f,1 exp(−∥ν − ν′∥2  2/L1),  k(2)((x, w), (x′, w′)) = σ2  f,2 exp(−∥ν − ν′∥2  2/L2),  where ν = (x, w) and ν′ = (x′, w′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Moreover, we used the L1-norm as the distance between distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In  all experiments except computational time experiments, we used the following two indicators R1 and R2 based  on (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2) to evaluate the goodness of ˆΠt estimated by each method:  R1 = inf{a ∈ R | F (ˆΠt) ⊂ Za},  R2 = inf{a ∈ R | Par(F (ˆΠt)) ⊂ Za}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Experimental details and additional experiments, which are not included in the main body, are described in  Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  7  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Synthetic Function  We evaluate the performance in our proposed method through synthetic functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' First, the input space  X × Ω was a set of 50 × 50 grid points equally spaced in [−10, 10] × [−10, 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In this experiment, we used the  following (scaled) Himmelblau’s function f (1)(x, w), which is commonly used as a benchmark function in BO  studies [Andrei, 2008], and sinusoidal function f (2)(x, w) as black-box functions:  f (1)(x, w) = (x2 + w − 11)2  150  + (x + w2 − 7)2  150  − C,  f (2)(x, w) = (80 sin(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5x) − 50 cos(2w))/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5,  where C = 3321.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='291/150 is a constant to set the mean to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Under this setting, we compared the following six methods:  Random: Determine the next evaluation point xt+1 at random.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  UCB F1: Select the next evaluation point by xt+1 = argmaxx∈X u(F (1))  t  (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  UCB F2: Select the next evaluation point by xt+1 = argmaxx∈X u(F (2))  t  (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  MVA: Select the next evaluation point by xt+1 = argmaxx∈Mt∪ˆΠt λt(x), where Mt and λt(x) are given in  Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2 of [Iwazaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2021].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  EHI: Select the next evaluation point xt+1 by maximizing an expected hypervolume improvement for the  DR-PF calculated based on posterior means.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Proposed: Select the next evaluation point xt+1 by Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Here, UCB F1 (or UCB F2) focuses on the maximization of F (1)(x) (or F (2)(x)) and does not consider the  identification of the DR-PF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In contrast, MVA focuses on reducing the uncertainty of a potential optimal set,  which is a set of input points that may constitute the DR-PF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The EHI method is the strategy that extends the  expected hypervolume improvement strategy, which is commonly used in BO for ordinary Pareto optimization  problems, to the DR-PF identification problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Because the expected hypervolume improvement for the DR-PF  cannot be calculated analytically, we approximated it using Monte Carlo sampling with a sample size of 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Experiments were conducted under the following two settings for the observation of w:  Simulator setting: At each time t, arbitrary w can be selected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Uncontrollable setting: At each time t, w cannot be selected and is observed as a random sample from the  uniform distribution on Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  The Simulator setting and Uncontrollable setting correspond to the development phase and use phase,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In Simulator setting, we used p∗(w) = 1/50, and the next environmental variable to be evaluate  for each method except Random was selected by  wt+1 = argmax  w∈Ω  (σ(1)2  t  (xt+1, w) + σ(2)2  t  (xt+1, w)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  In Random, wt+1 was selected as a random sample from the uniform distribution on Ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In Uncontrollable  setting, we allowed the use of a different reference distribution p∗  t (w) for each iteration t and used the empirical  distribution of w as p∗  t (w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Under this setup, one initial point was taken at random and the algorithm was run until the number of  iterations reached 500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' This simulation was repeated 100 times and the average values of R1 and R2 at each  iteration were calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' 3, it can be confirmed that R1 and R2 in Random are not zero even after  500 iterations for both settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In UCB F1 and UCB F2, the value of R1 is good but the value of R2 is  not good because they focus on one of the black-box functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' For MVA, EHI, and Proposed, which focus  on improving the DR-PF, R1 and R2 tend to be zero in both settings, but Proposed converges to zero more  quickly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Computational Time Experiments  We confirmed the computational time required to select xt+1 and wt+1 using each method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' We performed the  same experiment as in Simulator setting in the previous section to evaluate the computational time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Under  this setup, one initial point was taken at random and the algorithm was run until the number of iterations  reached 500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' We computed the average computational time over 500 iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' We also computed the ratio  of the computational time of each method to that of the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' From Table 1, it can be confirmed  that Random, which does not require inf calculations, is faster than the proposed method, and UCB F1 (or  8  UCB F2), which uses only u(F (1))  t  (x) (or u(F (2))  t  (x)) required inf calculations, is about half the computational  time of the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  The proposed method and MVA using both u(F (1))  t  (x) and u(F (2))  t  (x) have  comparable computational speed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' On the other hand, EHI, which performs the same number of inf calculations  for each Monte Carlo sample as the proposed method requires, takes about 100 times longer than the proposed  method because the number of Monte Carlo samples is 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Infection Simulation  We applied the proposed method to the Pareto optimization problem using a simulation model of a real-  world infectious disease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' We used the SIR model [Kermack and McKendrick, 1927], which is commonly used  as the infection simulation model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In this experiment, we used the SIR model which has the infection rate  β ∈ [0, 1] and the recovery γ ∈ [0, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The input space X × Ω was defined as the set of grid points when the  region [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5] × [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5] was equally divided into 50 × 50 grid points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Using the SIR model, we defined the  following two risk functions which can be interpreted as economic risks:  r1(β, γ) = n(β, γ) − 450β + 800γ − C1,  r2(β, γ) = n(β, γ) − C2,  where n(β, γ) is the maximum number of infected individuals during a given period, calculated using the SIR  model, and C1 and C2 are constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Notably, r1(β, γ) and r2(β, γ) were also used in [Inatsu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2022].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In  this experiment, we used the same parameter setting as them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' To adapt it to our problem setup, we multiplied  them by minus one because risk functions should be minimized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Because β and γ can be interpreted as both  design variables and environmental variables, we considered the following two cases:  Case1: f (1)(x, w) = −r1(x, w) and f (2)(x, w) = −r2(x, w), where x and w are the infection rate and recovery  rate, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Case2: f (1)(x, w) = −r1(x, w) and f (2)(x, w) = −r2(x, w), where x and w are the recovery rate and infection  rate, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  In this experiment, we considered Simulator setting as in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Under this setup, one initial point was taken at random and the algorithm was run until the number of  iterations reached 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' This simulation was repeated 100 times and the average values of R1 and R2 at each  iteration were calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' 4, it can be confirmed that the proposed method achieves equal or better  performance in all settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Conclusion  In this study, we proposed an efficient BO method for identifying the DR-PF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' We proved that the proposed  method has theoretical guarantees on accuracy and convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Furthermore, through numerical experiments,  we confirmed that the proposed method outperforms other comparative methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Future work includes extend-  ing the method to the case where w is a continuous random variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Acknowledgement  This work was partially supported by MEXT KAKENHI (20H00601), JST CREST (JPMJCR21D3, JP-  MJCR21D3), JST Moonshot R&D (JPMJMS2033-05), JST AIP Acceleration Research (JPMJCR21U2), NEDO  (JPNP18002, JPNP20006) and RIKEN Center for Advanced Intelligence Project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  References  [Amri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2021] Amri, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Riche, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Helbert, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Blanchet-Scalliet, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and Da Veiga, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' A  sampling criterion for constrained bayesian optimization with uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' arXiv preprint arXiv:2103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='05706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Andrei, 2008] Andrei, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' An unconstrained optimization test functions collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Optim,  10(1):147–161.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Beland and Nair, 2017] Beland, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' and Nair, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Bayesian optimization under uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In  NIPS BayesOpt 2017 workshop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Bogunovic et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2018] Bogunovic, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Scarlett, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Jegelka, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and Cevher, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Adversarially robust  optimization with Gaussian processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In Advances in neural information processing systems, pages 5760–  5770.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Emmerich, 2005] Emmerich, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Single-and multi-objective evolutionary design optimization assisted  by gaussian random field metamodels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' PhD thesis, Dortmund, Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Diss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  9  [Fr¨ohlich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2020] Fr¨ohlich, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Klenske, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Vinogradska, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Daniel, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and Zeilinger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Noisy-  input entropy search for efficient robust bayesian optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In Chiappa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' and Calandra, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', editors,  Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, volume  108 of Proceedings of Machine Learning Research, pages 2262–2272.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Gessner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2020] Gessner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Gonzalez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and Mahsereci, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Active multi-information source  Bayesian quadrature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In Uncertainty in Artificial Intelligence, pages 712–721.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Inatsu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2022] Inatsu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Takeno, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Karasuyama, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and Takeuchi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Bayesian optimization  for distributionally robust chance-constrained problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In Chaudhuri, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Jegelka, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Song, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Szepesvari,  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Niu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and Sabato, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', editors, Proceedings of the 39th International Conference on Machine Learning,  volume 162 of Proceedings of Machine Learning Research, pages 9602–9621.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Iwazaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2021] Iwazaki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Inatsu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and Takeuchi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Mean-variance analysis in bayesian opti-  mization under uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In Banerjee, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' and Fukumizu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', editors, Proceedings of The 24th International  Conference on Artificial Intelligence and Statistics, volume 130 of Proceedings of Machine Learning Research,  pages 973–981.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Kermack and McKendrick, 1927] Kermack, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' and McKendrick, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (1927).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  A contribution to the  mathematical theory of epidemics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Proceedings of the royal society of london.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Series A, Containing papers of  a mathematical and physical character, 115(772):700–721.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Kirschner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2020] Kirschner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Bogunovic, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Jegelka, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and Krause, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Distributionally robust  Bayesian optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In Chiappa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' and Calandra, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', editors, Proceedings of the Twenty Third Interna-  tional Conference on Artificial Intelligence and Statistics, volume 108 of Proceedings of Machine Learning  Research, pages 2174–2184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Kirschner and Krause, 2018] Kirschner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' and Krause, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Information directed sampling and bandits  with heteroscedastic noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In Conference On Learning Theory, pages 358–384.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Nguyen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2020] Nguyen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Gupta, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Ha, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Rana, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and Venkatesh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Distributionally  robust Bayesian quadrature optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  In Chiappa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' and Calandra, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', editors, Proceedings of the  Twenty Third International Conference on Artificial Intelligence and Statistics, volume 108 of Proceedings of  Machine Learning Research, pages 1921–1931.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Oliveira et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2019] Oliveira, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Ott, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and Ramos, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Bayesian optimisation under uncertain  inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In The 22nd International Conference on Artificial Intelligence and Statistics, pages 1177–1184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Qing et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2022] Qing, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Couckuyt, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and Dhaene, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' A robust multi-objective bayesian optimiza-  tion framework considering input uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='12848.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Rahimian and Mehrotra, 2019] Rahimian, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' and Mehrotra, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Distributionally robust optimization:  A review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' arXiv preprint arXiv:1908.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='05659.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Scarf, 1958] Scarf, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (1958).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' A min-max solution of an inventory problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Studies in the mathematical theory  of inventory and production, 10:201–209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Settles, 2009] Settles, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Active learning literature survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Technical report, University of Wisconsin-  Madison Department of Computer Sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Shahriari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2016] Shahriari, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Swersky, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Adams, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and De Freitas, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Taking  the human out of the loop: A review of Bayesian optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Proceedings of the IEEE, 104(1):148–175.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Srinivas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2010] Srinivas, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Krause, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Kakade, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and Seeger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Gaussian process optimization  in the bandit setting: No regret and experimental design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In Proceedings of the 27th International Conference  on International Conference on Machine Learning, ICML’10, pages 1015–1022, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Omnipress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Suzuki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2020] Suzuki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Takeno, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Tamura, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Shitara, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and Karasuyama, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Multi-  objective bayesian optimization using pareto-frontier entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In International Conference on Machine Learn-  ing, pages 9279–9288.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' PMLR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Toscano-Palmerin and Frazier, 2018] Toscano-Palmerin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' and Frazier, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Bayesian optimization  with expensive integrands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' arXiv preprint arXiv:1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='08661.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Williams and Rasmussen, 2006] Williams, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' and Rasmussen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Gaussian processes for machine  learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' the MIT Press, 2(3):4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  [Zuluaga et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2016] Zuluaga, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', Krause, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', and P¨uschel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' ε-pal: an active learning approach to  the multi-objective optimization problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The Journal of Machine Learning Research, 17(1):3619–3650.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  10  Appendix  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Generalization of Problem Setup  Here, we consider a more general problem setting, including the setting introduced in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Specif-  ically, we consider the following three settings:  The case with three or more objective functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Environment variables cannot be controlled even during optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  The setting where reference distributions, control parameter ξ, and candidate distribution family A set  differently at each time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Furthermore, by combining (ii) and (iii), we show that under appropriate assumptions, the solution to the  distributionally robust Pareto optimization problem is also a good solution to the Pareto optimization problem  defined by the true expectation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Extended Problem Setting  Let f (1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , f (m) : X × Ω → R be expensive-to-evaluate black-box functions, where 2 ≤ m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Also let X and  Ω be finite sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Here, for each (x, w) ∈ X ×Ω and j ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , m} ≡ [m], the value of f (j)(x, w) is observed with  Gaussian noise ε(j) as y(j) = f (j)(x, w) + ε(j), where ε(1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , ε(m) are mutually independent, and ε(j) follows  Normal distribution with mean zero and variance σ(j)2  noise, that is, ε(j) ∼ N(0, σ(j)2  noise).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In this section, we assume  that w ∈ Ω is a discrete random variable and follows some unknown distribution P †.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Here, for environmental  variables, we consider either settings in the development phase or settings in the use phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' That is, in the  former, environmental variables are completely controllable as design variables;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' in the latter, environmental  variables are uncontrollable and observed as realizations from the true distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Furthermore, let At denote  the candidate distribution family of P † at each time t, and consider the following At:  At = {p(w) | d(p(w), p∗  t (w)) ≤ ξt},  where p∗  t (w) is a user-specified reference distribution, d(·, ·) is a given distance function between distribu-  tions, and ξt ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, for each design variable x ∈ X and time t, the distributionally robust expectations  F (1)  t  (x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , F (m)  t  (x) are defined as follows:  F (j)  t  (x) =  inf  p(w)∈At  �  w∈Ω  f (j)(x, w)p(w), j ∈ [m].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Hereafter, we aim to efficiently identify the PF Z∗  t determined by F (1)  t  (x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , F (m)  t  (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' For each x ∈ X, subset  E ⊂ X and time t, let Ft(x) = (F (1)  t  (x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , F (m)  t  (x)) and Ft(E) = {Ft(x) | x ∈ E}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Moreover, for a set  B ⊂ Rm, the domain Dom(B) dominated by B and the Pareto-frontier Par(B) of B are given by  Dom(B) = {y ∈ Rm |∃ y′ ∈ B s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' y ⪯ y′},  Par(B) = ∂(Dom(B)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Then, the PF Z∗  t defined by F (1)  t  (x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , F (m)  t  (x) can be expressed as follows:  Z∗  t = Par(Ft(X)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Gaussian Process  Next, we construct predictive models for the black-box functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  As in the main body, GPs are used to  model the black-box functions f (1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , f (m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' First, for each j ∈ [m], assume that f (j) follows a GP prior  GP(0, k(j)((x, w), (x′, w′))), where k(j)((x, w), (x′, w′)) is a positive-definite kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Then, under the given  dataset {(xi, wi, y(j)  i )}t  i=1, the posterior distribution of f (j) is again a GP, and its posterior mean µ(j)  t (x, w)  and posterior variance σ(j)2  t  (x, w) are given by  µ(j)  t (x, w) = k(j)  t (x, w)⊤(K(j)  t  + σ(j)2  noiseIt)−1y(j)  t ,  σ(j)2  t  (x, w) = k(j)((x, w), (x, w)) − k(j)  t (x, w)⊤(K(j)  t  + σ(j)2  noiseIt)−1k(j)  t (x, w),  where k(j)  t (x, w) is the t-dimensional vector whose kth element is k(j)((x, w), (xk, wk)), y(j)  t  = (y(j)  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , y(j)  t )⊤,  K(j)  t  is the t × t matrix whose (k, l)th element is k(j)((xk, wk), (xl, wl)) and It is the t × t identity matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  11  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Proposed Method in the Generalized Setting  Here, we propose a BO method for efficiently identifying Z∗  t .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Using the same argument as the method used in  the main body, we construct credible intervals interval for F (1)  t  (x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , F (m)  t  (x) using the method proposed by  [Kirschner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2020], and give an estimation method for the PF based on the constructed credible intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Composition of Credible Intervals and Pareto-frontier Estimation  For each (x, w) ∈ X ×Ω, j ∈ [m] and time t, let Q(f (j))  t  (x, w) = [l(f (j))  t  (x, w), u(f (j))  t  (x, w)] be a credible interval  of f (j)(x, w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Here, l(f (j))  t  (x, w) and u(f (j))  t  (x, w) are given by  l(f (j))  t  (x, w) = µ(j)  t (x, w) − β1/2  j,t σ(j)  t (x, w),  u(f (j))  t  (x, w) = µ(j)  t (x, w) + β1/2  j,t σ(j)  t (x, w),  where β1/2  j,t ≥ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, the credible interval for F (j)  t  (x) is denoted as Q(F (j)  t  )  t  (x) ≡ [l(F (j)  t  )  t  (x), u(F (j)  t  )  t  (x)], where  its lower and upper are given by  l  (F (j)  j  )  t  (x) =  inf  p(w)∈At  �  w∈Ω  l(f (j))  t  (x, w)p(w),  u  (F (j)  j  )  t  (x) =  inf  p(w)∈At  �  w∈Ω  u(f (j))  t  (x, w)p(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Next, for each x ∈ X, subset E ⊂ X and time t, we define LCB(m)  t  (x), UCB(m)  t  (x) and LCB(m)  t  (E) as  LCB(m)  t  (x) = (l(F (1)  t  )  t  (x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , l(F (m)  t  )  t  (x)), UCB(m)  t  (x) = (u(F (1)  t  )  t  (x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , u(F (m)  t  )  t  (x)),  LCB(m)  t  (E) = {LCB(m)  t  (x) | x ∈ E}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Using this, we define the estimated Pareto solutions set ˆΠ(m)  t  ⊂ X for design variables as  ˆΠ(m)  t  = {x ∈ X | LCB(m)  t  (x) ∈ Par(LCB(m)  t  (X))}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Hereafter, for simplicity, we denote LCB(m)  t  (x), UCB(m)  t  (x), LCB(m)  t  (E) and ˆΠ(m)  t  as LCBt(x), UCBt(x),  LCBt(E) and ˆΠt, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Acquisition Function  Here, we propose an AF to determine the next evaluation point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Similar to the main body, we define the AF  at(x) for x ∈ X as  at(x) = dist(UCBt(x), Dom(LCBt(ˆΠt))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Then, the next evaluation point is selected as follows:  Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1 (For the setting in the development phase).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The next design variable xt+1 to be evaluated is  selected by  xt+1 = argmax  x∈X  at(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Similarly, the next environmental variable wt+1 to be evaluated is selected by  wt+1 = argmax  w∈Ω  {σ(1)2  t  (xt+1, w) + · · · + σ(m)2  t  (xt+1, w)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Notably, since wt+1 cannot be selected in the setting at the use phase, wt+1 is the realized value from P †  at time t + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Here, at(x) can be computed analytically by the following lemma:  Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Let UCBt(x) = (u1, , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , um) and LCBt(ˆΠt) = {(l(i)  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , l(i)  m ) | 1 ≤ i ≤ k}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, at(x) can  be computed as follows:  at(x) = max{˜at(x), 0},  ˜at(x) = min  1≤i≤k max{u1 − l(i)  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , um − l(i)  m }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Stopping Condition  Here, we give a stopping condition of our proposed algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' As in the main body, let ϵ > 0 be a user-  specified stopping parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, algorithms terminate if at(x) ≤ ϵ is satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Finally, the pseudo-codes  of the proposed algorithm in the development phase and use phase settings are given in Algorithm 2 and 3,  respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  12  Algorithm 2 BO for identifying DR-PF in the development phase setting  Input: GP prior GP(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' k(j)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' candidate distribution family At,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' tradeoff parameter {βj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='t}t≥0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' stopping param-  eter ϵ > 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' j ∈ [m]  t ← 1  while at(x) > ϵ do  Compute Q(F (j)  t  )  t  (x) for each x ∈ X and j ∈ [m]  Select the next evaluation point (xt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' wt)  Observe y(j)  t  = f (j)(xt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' wt) + ε(j)  t  for each j ∈ [m]  Update GPs by adding observed points  t ← t + 1  end while  Output: Return ˆΠt as the estimated set of design variables comprising the DR-PF  Algorithm 3 BO for identifying DR-PF in the use phase setting  Input: GP prior GP(0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' k(j)),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' candidate distribution family At,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' tradeoff parameter {βj,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='t}t≥0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' stopping param-  eter ϵ > 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' j ∈ [m]  t ← 1  while at(x) > ϵ do  Compute Q(F (j)  t  )  t  (x) for each x ∈ X and j ∈ [m]  Select the next evaluation point xt  Generate wt from P †  Observe y(j)  t  = f (j)(xt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' wt) + ε(j)  t  for each j ∈ [m]  Update GPs by adding observed points  t ← t + 1  end while  Output: Return ˆΠt as the estimated set of design variables comprising the DR-PF  A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Theoretical Analysis  Here, we give theorems on the accuracy and convergence of the proposed algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' First, to give theoretical  guarantees, we assume that for each j ∈ [m], f (j) follows GP GP(0, k(j)((x, w), (x′, w′))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In addition, we assume  that each prior variance k(j)((x, w), (x, w)) ≡ σ(j)2  0  (x, w) satisfies  max  (x,w)∈X×Ω σ(j)2  0  (x, w) ≤ 1,  ∀j ∈ [m].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Furthermore, let κ(j)  T  be a maximum information gain for f (j) at time T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Moreover, as in the main body,  we define an ϵ-accurate Pareto region Zϵ,t to quantify the goodness of the predicted ˆΠt as input points that  constitute the PF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' For a positive number ϵ and the m-dimensional vector ϵ = (ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , ϵ), we define Zϵ,t as  Zϵ,t = {y ∈ Rm |∃ y′ ∈ Z∗  t s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' y ⪯ y′ and ∃y′′ ∈ Z∗  t s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' y′′ ⪯ y + ϵ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Using Zϵ,t, we define the accuracy of ˆΠt as follows:  Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2 (Accuracy for ˆΠt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Let ϵ be a positive number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Then, we define ˆΠt to be an ϵ-accurate  estimated solution set if the following holds:  Ft(ˆΠt) ⊂ Zϵ,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1)  In addition, we define ˆΠt to be an ϵ-accurate estimated Pareto solution set if the following holds:  Par(Ft(ˆΠt)) ⊂ Zϵ,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2)  Then, the following theorem guarantees that the proposed algorithms satisfy both (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1) and (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2) with a  high probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Let t ≥ 1 and δ ∈ (0, 1), and define β1,t = · · · = βm,t = 2 log(m|X × Ω|π2t2/(6δ)) ≡ βt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Moreover, let ϵ > 0 be a user-specified stopping parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Then, when Algorithm 2 terminates, with a  probability of at least 1 − δ, ˆΠt satisfies both (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1) and (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2) for any At.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Next, we give a theorem on convergence in the development phase setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' The following theorem gives  convergence guarantees for Algorithm 2:  13  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Under the same condition as in Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1, let T be the smallest positive integer satisfying  the following inequality:  βT (C1κ(1)  T  + · · · + Cmκ(m)  T  )  T  ≤ ϵ2  4 ,  where Cj = 2/ log(1 + σ(j)−2  noise ) and j ∈ [m].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, Algorithm 2 terminates after at most T iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Next, we give the theorem on convergence under the setting in the use phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Unlike the setting in the  development phase, we cannot control w in the use phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Therefore, to make a reasonable inference, the  uncertainty at all points must be able to be reduced stochastically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' However, if the value of the true probability  function p†(w) at some w ∈ Ω is zero, the uncertainty of f (j)(x, w) containing this point cannot be sufficiently  small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' To avoid this problem, we make the following assumption on the true probability function:  min  w∈Ω p†(w) ≡ pmin > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Then, the following theorem holds:  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Under the same condition as in Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1, assume that pmin > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Let T be the smallest  positive integer satisfying the following inequality:  βT ( ˜C1κ(1)  T  + · · · + ˜Cmκ(m)  T  + ˜C)  T  ≤ ϵ2  4 ,  where ˜Cj = (4p−1  min)/ log(1 + σ(j)−2  noise ), ˜C = 8mp−1  min log(8m/δ) and j ∈ [m].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, with a probability of at least  1 − δ, Algorithm 3 terminates after at most T trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Finally, we show that under appropriate assumptions, the solution to the distributionally robust Pareto  optimization problem is also a good solution to the Pareto optimization problem defined by the true expectation  in the use phase setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Here, the expectation function ˜F (j)(x) determined by the true probability function  p†(w) is given by  ˜F (j)(x) =  �  w∈Ω  f (j)(x, w)p†(w), j ∈ [m].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  In addition, for each x ∈ X and E ⊂ X, let ˜F (x) = ( ˜F (1)(x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , ˜F (m)(x)) and ˜F (E) = { ˜F (x) | x ∈ E}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Then, the PF ˜Z∗ defined by ˜F (1)(x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , ˜F (m)(x) can be expressed as follows:  ˜Z∗ = Par( ˜F (X)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Furthermore, as in the case of Z∗  t , we define an ϵ-accurate Pareto region ˜Zϵ for ˜Z∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' For a positive number ϵ  and an m-dimensional vector ϵ = (ϵ, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , ϵ), we define ˜Zϵ as  ˜Zϵ = {y ∈ Rm |∃ y′ ∈ ˜Z∗ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' y ⪯ y′ and ∃y′′ ∈ ˜Z∗ s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' y′′ ⪯ y + ϵ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Using ˜Zϵ, we define the accuracy of ˆΠt for ˜Z∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Definition A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3 (Accuracy of ˆΠt for ˜Z∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Let ϵ be a positive number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, we define ˆΠt to be an ϵ-accurate  estimated solution set for ˜Z∗ if the following holds:  Ft(ˆΠt) ⊂ ˜Zϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Moreover, we define ˆΠt to be an ϵ-accurate estimated Pareto solution set for ˜Z∗ if the following holds:  Par(Ft(ˆΠt)) ⊂ ˜Zϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Then, the following theorem holds:  Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Under the use phase setting, let t ≥ 1 and δ ∈ (0, 1), and define β1,t = · · · = βm,t =  2 log(m|X × Ω|π2t2/(6δ)) ≡ βt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Moreover, let ϵ > 0 be a user-specified stopping parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Furthermore, let  the reference distribution p∗  t (w) be the empirical distribution function for w, and define ξt and the distance  between distributions d(·, ·) as  ξt = |Ω|  �  1  2t log  �|Ω|π2t2  3δ  �  ,  d(p1(w), p2(w)) =  �  w∈Ω  |p1(w) − p2(w)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Then, if Algorithm 3 terminates at t ≥ T after time T, with a probability of at least 1−2δ, ˆΠt is the 2ϵ-accurate  estimated set and estimated Pareto set, that is, the following holds:  Ft(ˆΠt) ⊂ ˜Z2ϵ,  Par(Ft(ˆΠt)) ⊂ ˜Z2ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Here, T is the smallest positive integer satisfying the following inequality:  ∀n ≥ T, 2β1/2  1  ξn ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3)  14  B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Proofs  Here, we give proofs of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1 and Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1–A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Notably, Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1 and Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2 in the  main body are special cases of Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1 and Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1–A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' First, we prove Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Let UCBt(x) = (u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , um) ≡ u and LCBt(ˆΠt) = {(l(i)  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , l(i)  m ) | 1 ≤ i ≤ k} ≡ L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Here, if  u ∈ Dom(L), then the following holds from the definition of dist(a, B):  at(x) = dist(u, Dom(L)) =  inf  b∈Dom(L) d∞(u, b) = d∞(u, u) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  In addition, since u ∈ Dom(L), there exists (l(i)  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , l(i)  m ) such that uj ≤ l(i)  j  for any j ∈ [m].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Thus, we have  max{u1 − l(i)  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , um − l(i)  m } ≤ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' This implies that  ˜at(x) = min  1≤i≤k max{u1 − l(i)  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , um − l(i)  m } ≤ 0  and max{˜at(x), 0} = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Therefore, we get at(x) = max{˜at(x), 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Next, we consider the case where u /∈  Dom(L).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Let at(x) = η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, noting that u /∈ Dom(L), for any i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , k}, there exists j ∈ [m] such that  uj > l(i)  j .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' This implies that  ˜at(x) = min  1≤i≤k max{u1 − l(i)  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , um − l(i)  m } ≡ ˜η > 0  and max{˜at(x), 0} = ˜at(x) = ˜η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' For this ˜η, there exists i such that  uj − l(i)  j  ≤ ˜η  ∀j ∈ [m].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Hence, we have ˜u ≡ (u1 − ˜η, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , um − ˜η) ∈ Dom(L) because uj − ˜η ≤ l(i)  j  for any j ∈ [m].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Thus, from the  definition of at(x), the following holds:  η = at(x) = dist(u, Dom(L)) =  inf  b∈Dom(L) d∞(u, b) ≤ d∞(u, ˜u) = ˜η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Here, we assume η < ˜η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, noting that Dom(L) is the closed set, there exists ˜l = (˜l1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , ˜lm) ∈ Dom(L)  such that d∞(u, ˜l) = η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Therefore, ˜l can be expressed as ˜l = (u1 − s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , um − sm), where 0 ≤ |sj| ≤ η and at  least one of s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , sm is η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Thus, since (u1 − η, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , um − η) ⪯ ˜l, noting that (u1 − η, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , um − η) ∈ Dom(L)  there exists i such that  uj − η ≤ l(i)  j  ∀j ∈ [m].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  This implies that max{u1 − l(i)  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , um − l(i)  m } ≤ η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Hence, it follows that  ˜η = min  1≤i≤k max{u1 − l(i)  1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , um − l(i)  m } ≤ η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  However, this is a contradiction with η < ˜η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Consequently, we obtain at(x) = max{˜at(x), 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Next, we prove Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' First, we prove Ft(ˆΠt) ⊂ Zϵ,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Since ˆΠt ⊂ X, for any y ∈ Ft(ˆΠt), there exists y′ ∈ Z∗  t such that  y ⪯ y′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Thus, it is sufficient to show that there exists y′′ ∈ Z∗  t such that y′′ ⪯ y +ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Here, under the theorem’s  assumption, with a probability of at least 1 − δ, the following holds for any (x, w) ∈ X × Ω, j ∈ [m] and time  t ≥ 1:  f (j)(x, w) ∈ Q(f (j))  t  (x, w),  where this relation can be derived by using Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1 of [Srinivas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2010].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Hence, we have F (j)  t  (x) ∈  Q(F (j)  t  )  t  (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In addition, since Z∗  t is the closed set, for any x ∈ ˆΠt, there exist a ≥ 0 and Ft(x) + (a, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , a) ≡  y′′ ∈ Z∗  t such that  dist(Ft(x), Z∗  t ) = d∞(Ft(x), y′′) ≤ d∞((l(F (1)  t  )  t  (x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , l(F (m)  t  )  t  (x)), y′′′),  where y′′′ ∈ Z∗  t can be given by using s ≥ a ≥ 0 as y′′′ = (l(F (1)  t  )  t  (x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , l(F (m)  t  )  t  (x)) + (s, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Here, for some  ˆx ∈ X satisfying y′′′ ⪯ Ft(ˆx), the following holds:  d∞((l(F (1)  t  )  t  (x), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , l(F (m)  t  )  t  (x)), y′′′) ≤ dist(Ft(ˆx), Dom(LCBt(ˆΠt))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  15  Moreover, the right hand side is bounded from above as  dist(Ft(ˆx), Dom(LCBt(ˆΠt)))  ≤ dist(UCBt(ˆx), Dom(LCBt(ˆΠt)))  ≤ max  x†∈X dist(UCBt(x†), Dom(LCBt(ˆΠt))) = at(xt+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Therefore, if at(xt+1) ≤ ϵ, then d∞(Ft(x), y′′) ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' It follows that y′′ ⪯ Ft(x) + ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Since x is an arbitrary  element of ˆΠt, we have Ft(ˆΠt) ⊂ Zϵ,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Next, we prove Par(Ft(ˆΠt)) ⊂ Zϵ,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' As before, noting that ˆΠt ⊂ X, for  any y ∈ Par(Ft(ˆΠt)), there exists y′ ∈ Z∗  t such that y ⪯ y′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In addition, since Z∗  t is the closed set, for any  y ∈ Par(Ft(ˆΠt)), there exist a ≥ 0 and y + (a, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , a) ≡ y′′ ∈ Z∗  t such that  dist(y, Z∗  t ) = d∞(y, y′′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Here, for some ˆx ∈ X satisfying y′′ ⪯ Ft(ˆx), the following holds:  d∞(y, y′′) ≤ d∞(y′′′, Ft(ˆx)) ≤ dist(Ft(ˆx), Dom(LCBt(ˆΠt))),  where y′′′ ∈ Par(Ft(ˆΠt)) can be given by using s′ ≥ a ≥ 0 as y′′′ = Ft(ˆx) − (s′, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , s′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, we obtain  dist(Ft(ˆx), Dom(LCBt(ˆΠt)))  ≤ dist(UCBt(ˆx), Dom(LCBt(ˆΠt)))  ≤ max  x†∈X dist(UCBt(x†), Dom(LCBt(ˆΠt))) = at(xt+1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Thus, if at(xt+1) ≤ ϵ, then d∞(y, y′′) ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' This implies that y′′ ⪯ y + ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Consequently, since y is an arbitrary  element of Par(Ft(ˆΠt)), we have Par(Ft(ˆΠt)) ⊂ Zϵ,t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Next, we prove Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Let xt = argmaxx∈X at−1(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Here, since LCB t−1(xt) ∈ Dom(LCB t−1(ˆΠt−1)), the following in-  equality holds:  at−1(xt) = dist(UCBt−1(xt), Dom(LCB t−1(ˆΠt−1)))  ≤ d∞(UCB t−1(xt), LCB t−1(xt))  = max  1≤j≤m{u  (F (j)  t−1)  t−1  (xt) − l  (F (j)  t−1)  t−1  (xt)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Therefore, from the definition of u  (F (j)  t−1)  t−1  (xt) and l  (F (j)  t−1)  t−1  (xt), we get  u  (F (j)  t−1)  t−1  (xt) − l  (F (j)  t−1)  t−1  (xt) ≤ 2β1/2  t  max  w∈Ω σ(j)  t−1(xt, w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Hence, the following inequality holds:  a2  t−1(xt) ≤ 4βt max  1≤j≤m max  w∈Ω σ(j)2  t−1 (xt, w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Furthermore, since wt is selected by  wt = argmax  w∈Ω  (σ(1)2  t−1 (xt, w) + · · · + σ(m)2  t−1 (xt, w)),  the following holds:  a2  t−1(xt) ≤ 4βt max  1≤j≤m max  w∈Ω σ(j)2  t−1 (xt, w)  ≤ 4βt(σ(1)2  t−1 (xt, wt) + · · · + σ(m)2  t��1 (xt, wt)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  In addition, let T be the number given by Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, we get  T min  1≤t≤T a2  t−1(xt) ≤  T  �  t=1  a2  t−1(xt)  ≤ 4βT  m  �  j=1  T  �  t=1  σ(j)2  t−1 (xt, wt)  ≤ 4βT (C1κ(1)  T  + · · · + Cmκ(m)  T  ),  16  where the last inequality can be derived by using Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4 of [Srinivas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2010].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Therefore,  dividing both sides by T, we obtain  min  1≤t≤T a2  t−1(xt) ≤ 4βT  C1κ(1)  T  + · · · + Cmκ(m)  T  T  ≤ ϵ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Hence, we get min1≤t≤T at−1(xt) ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' This implies that there exists t′ ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , T} such that at′−1(xt′) ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Next, we prove Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Using the same argument as in the proof of Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2, we have  a2  t−1(xt) ≤ 4βt max  1≤j≤m max  w∈Ω σ(j)2  t−1 (xt, w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Furthermore, since pmin > 0, the following inequality holds:  max  w∈Ω σ(j)2  t−1 (xt, w) ≤  �  wΩ  σ(j)2  t−1 (xt, w)  =  �  wΩ  (p†(w))−1p†(w)σ(j)2  t−1 (xt, w)  ≤ p−1  min  �  wΩ  p†(w)σ(j)2  t−1 (xt, w)  ≡ p−1  minEw[σ(j)2  t−1 (xt, w)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Using this, we get  max  1≤j≤m max  w∈Ω σ(j)2  t−1 (xt, w) ≤  m  �  j=1  max  w∈Ω σ(j)2  t−1 (xt, w)  ≤ p−1  min  m  �  j=1  Ew[σ(j)2  t−1 (xt, w)]  = p−1  minEw  �  �  m  �  j=1  σ(j)2  t−1 (xt, w)  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Here, let T be the number given by Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, we obtain  T min  1≤t≤T a2  t−1(xt) ≤  T  �  t=1  a2  t−1(xt)  ≤ 4βT p−1  min  T  �  t=1  Ew  �  �  m  �  j=1  σ(j)2  t−1 (xt, w)  �  � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1)  Noting that �m  j=1 σ(j)2  t−1 (xt, w) is a non-negative random variable and �m  j=1 σ(j)2  t−1 (xt, w) ≤ m, from Lemma 3  of [Kirschner and Krause, 2018], the following holds with a probability of at least 1 − δ:  T  �  t=1  Ew  �  �  m  �  j=1  σ(j)2  t−1 (xt, w)  �  � ≤ 2  m  �  j=1  T  �  t=1  σ(j)2  t−1 (xt, w) + 4m log 1  δ + 8m log 4m + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Moreover, since 4m log 1  δ ≤ 8m log 1  δ and 1 ≤ 8m log 2, we have  4m log 1  δ + 8m log 4m + 1 ≤ 8m log 1  δ + 8m log 4m + 8m log 2  = 8m log 8m  δ  and  T  �  t=1  Ew  �  �  m  �  j=1  σ(j)2  t−1 (xt, w)  �  � ≤ 2  m  �  j=1  T  �  t=1  σ(j)2  t−1 (xt, w) + 8m log 8m  δ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2)  17  Hence, by substituting (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2) into (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1), from Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4 of [Srinivas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2010], we get  T min  1≤t≤T a2  t−1(xt) ≤ 4βT ( ˜C1κ(1)  T  + · · · + ˜Cmκ(m)  T  + ˜C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Therefore, from the definition of T, dividing both sides by T, we obtain  min  1≤t≤T a2  t−1(xt) ≤ 4βT  ˜C1κ(1)  T  + · · · + ˜Cmκ(m)  T  + ˜C  T  ≤ ϵ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Thus, we get min1≤t≤T at−1(xt) ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' This implies that there exists t′ ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , T} such that at′−1(xt′) ≤ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Finally, we prove Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Suppose that p∗  t (w) is the empirical distribution function of w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, from Hoeffding’s inequality, the  following inequality holds for any w:  P(|p∗  t (w) − p†(w)| ≥ λ) ≤ 2 exp(−2tλ2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Here, let  λ =  �  1  2t log  �|Ω|π2t2  3δ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Then, with a probability of at least 1 − δ, the following holds for any t ≥ 1 and w ∈ Ω:  |p∗  t (w) − p†(w)| ≤ λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  In addition, from the definition of d(·, ·), we get  d(p∗  t (w), p†(w)) =  �  w∈Ω  |p∗  t (w) − p†(w)| ≤ |Ω|λ = ξt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  This implies that p†(w) ∈ At.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Furthermore, from the definition of ˜F (j)(x) and F (j)  t  (x), the following inequality  holds for any t ≥ 1, j ∈ [m] and x ∈ X:  F (j)  t  (x) ≤ ˜F (j)(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Therefore, it follows that  Ft(x) ⪯ ˜F (x)  ∀x ∈ X,∀ t ≥ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3)  Here, for any x ∈ X, t ≥ 1 and j ∈ [m], let ¯p(j)  t,x(w) ∈ At be the probability function satisfying  F (j)  t  (x) =  �  w∈Ω  f (j)(x, w)¯p(j)  t,x(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Then, the following inequality holds:  | ˜F (j)(x) − F (j)  t  (x)| ≤  �  w∈Ω  |f (j)(x, w)||p†(w) − ¯p(j)  t,x(w)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Moreover, from Lemma 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1 of [Srinivas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=', 2010], with a probability of at least 1 − δ, the following holds for  any x ∈ X, w ∈ Ω and j ∈ [m]:  |f (j)(x, w)| ≤ β1/2  1  σ(j)  0 (x, w) ≤ β1/2  1  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Hence, we have  ˜F (j)(x) − F (j)  t  (x) ≤ | ˜F (j)(x) − F (j)  t  (x)|  ≤ β1/2  1  �  w∈Ω  |p†(w) − ¯p(j)  t,x(w)|  = β1/2  1  d(p†(w), ¯p(j)  t,x(w))  ≤ β1/2  1  (d(p†(w), p∗  t (w)) + d(p∗  t (w), ¯p(j)  t,x(w))) ≤ 2β1/2  1  ξt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  In addition, let T be the smallest positive integer satisfying (A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, for any t ≥ T, the following inequality  holds:  ˜F (j)(x) ≤ F (j)  t  (x) + ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  18  Thus, we obtain  ˜F (x) ⪯ Ft(x) + ϵ  ∀x ∈ X,∀ t ≥ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4)  Therefore, by combining (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='3) and (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='4), we have  Par(Ft(X)) ⊂ ˜Zϵ  ∀t ≥ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5)  Finally, from Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1, the following holds at t′, the time at which the algorithm terminates:  Ft′(ˆΠt′) ⊂ Zϵ,t′, Par(Ft′(ˆΠt′)) ⊂ Zϵ,t′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6)  Consequently, if t′ ≥ T, using (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='5) and (B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='6) we get  Ft′(ˆΠt′) ⊂ ˜Z2ϵ, Par(Ft′(ˆΠt′)) ⊂ ˜Z2ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Experimental Details and Additional Experiments  Here, we give experimental details and additional experiments in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Experimental Setup  The experimental parameters used in each experiment are described in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Table 2: Experimental parameters for each setting  Parameters  Simulator setting  σ2  f,1 = 1000, L1 = 2, σ(1)2  noise = 10−4, β1/2  1,t = 3, σ2  f,2 = 1000, L2 = 2, σ(2)2  noise = 10−4, β1/2  2,t = 3, ξ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='05  Uncontrollable setting  σ2  f,1 = 1000, L1 = 2, σ(1)2  noise = 10−4, β1/2  1,t = 3, σ2  f,2 = 1000, L2 = 2, σ(2)2  noise = 10−4, β1/2  2,t = 3, ξ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='05  SIR (Case1)  σ2  f,1 = 5000, L1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1, σ(1)2  noise = 10−8, β1/2  1,t = 3, σ2  f,2 = 105, L2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='01, σ(2)2  noise = 10−4, β1/2  2,t = 2, ξ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  SIR (Case2)  σ2  f,1 = 104, L1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1, σ(1)2  noise = 10−3, β1/2  1,t = 2, σ2  f,2 = 105, L2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='1, σ(2)2  noise = 10−3, β1/2  2,t = 3, ξ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  MVA  The MVA method is based on reducing the uncertainty in the potential optimal set Mt and the  estimated PF solution set ˆΠt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Using ˆΠt, Mt is defined as follows:  Mt = {x ∈ X \\ ˆΠt |∀ x′ ∈ ˆΠt, u(F (1))  t  (x) > l(F (1))  t  (x′) or u(F (2))  t  (x) > l(F (2))  t  (x′)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  The uncertainty λt(x) is given by  λt(x) =  �  (u(F (1))  t  (x) − l(F (1))  t  (x))2 + (u(F (2))  t  (x) − l(F (2))  t  (x))2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  EHI  The EHI method is based on the expected hypervolume improvement for a bounded region defined by  PFs and reference points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Let B ⊂ R2 be a set, and let r = (r1, r2) ∈ R2 be a reference point satisfying r ⪯ B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Then, let us denote the bounded region dominated by B and r, by  Dom(B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' r) = Dom(B) ∩ [r1, ∞) × [r2, ∞).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  In EHI, for each j ∈ {1, 2} we calculated the estimated value of F (j)(x) by using posterior means as  µ(F (j))  t  (x) =  inf  p(w)∈A  �  w∈Ω  µ(j)  t (x, w)p(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  For a point x ∈ X a subset E ⊂ X, we define µ(F )  t  (x) and µ(F )  t  (E) as  µ(F )  t  (x) = (µ(F (1))  t  (x), µ(F (2))  t  (x)),  µ(F )  t  (E) = {µ(F )  t  (x) | x ∈ E}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  In our experiments, we defined the reference point rt = (rt,1, rt,2) for each iteration t as  rt,1 = min  x∈X µ(F (1))  t  (x),  rt,2 = min  x∈X µ(F (2))  t  (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Then, the expected hypervolume improvement for x ∈ X is given by  EHIt(x) = EF (1)(x),F (2)(x)[Vol(Dom(µ(F )  t  (X) ∪ {(F (1)(x), F (2)(x))};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' rt) \\ Dom(µ(F )  t  (X);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' rt))].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  19  Table  3: Computational time (second) and computational time ratio for each setting when Nx = 50 and  Nw = 100  Random  UCB F1  UCB F2  MVA  EHI  Proposed  Computational time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='181  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='185  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='375  45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='77  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='364  (Standard error)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='001)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='001)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='001)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='025)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='001)  Computational time ratio  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='510  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='031  126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='15  1  (Standard error)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='002)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='002)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='003)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='327)  (0)  Table  4: Computational time (second) and computational time ratio for each setting when Nx = 100 and  Nw = 50  Random  UCB F1  UCB F2  MVA  EHI  Proposed  Computational time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='134  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='135  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='272  31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='97  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='268  (Standard error)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='001)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='001)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='001)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='015)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='001)  Computational time ratio  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='503  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='507  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='019  119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='92  1  (Standard error)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='002)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='002)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='004)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='346)  (0)  Table  5: Computational time (second) and computational time ratio for each setting when Nx = 100 and  Nw = 100  Random  UCB F1  UCB F2  MVA  EHI  Proposed  Computational time  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='360  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='362  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='719  91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='82  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='726  (Standard error)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='001)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='001)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='002)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='099)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='002)  Computational time ratio  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='496  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='500  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='991  127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='02  1  (Standard error)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='000)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='001)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='001)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='002)  (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='412)  (0)  Here, for a bounded set A, Vol(A) represents the hypervolume of A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Because F (1)(x) and F (2)(x) do not  follow GPs, we cannot calculate EHIt(x) analytically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Thus, we approximate it by using samples from posterior  distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Let M be a number of Monte Carlo sampling, and let (f (j)  t,(l)(x, w1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , f (j)  t,(l)(x, w|Ω|)) be an  lth sample from the posterior distribution of (f (j)(x, w1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' , f (j)(x, w|Ω|)) at iteration t, where 1 ≤ l ≤ M,  j ∈ {1, 2} and x ∈ X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' Then, for each t, we calculate F (1)  t,(l)(x) and F (2)  t,(l)(x) as  F (1)  t,(l)(x) =  inf  p(w)∈A  �  w∈Ω  f (1)  t,(l)(x, w)p(w),  F (2)  t,(l)(x) =  inf  p(w)∈A  �  w∈Ω  f (2)  t,(l)(x, w)p(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Using this, we approximate EHIt(x) as  1  M  M  �  l=1  Vol(Dom(µ(F )  t  (X) ∪ {(F (1)  t,(l)(x), F (2)  t,(l)(x))};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' rt) \\ Dom(µ(F )  t  (X);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' rt)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  Additional Computational Time Experiments  We also compared the computational time of each method  by changing input space settings conducted in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' In this experiment, the input space X × Ω was a set  of grid points divided into [−10, 10] × [−10, 10] equally spaced at Nx × Nw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' We compared computational times  using (50, 100), (100, 50) and (100, 100) as (Nx, Nw).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content=' From Table 3–5, it can be confirmed that the results are  similar to the experimental results conducted in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}
+page_content='  20' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/7dFJT4oBgHgl3EQfmywg/content/2301.11588v1.pdf'}