arxiv:1207.1386

Metrics for Markov Decision Processes with Infinite State Spaces

Published on Jul 4, 2012

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Abstract

Metrics for measuring state similarity in MDPs with infinite continuous state spaces provide a stable framework for planning and approximation, showing continuous variation of optimal value functions with respect to these metrics.

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We present metrics for measuring state similarity in Markov decision processes (MDPs) with infinitely many states, including MDPs with continuous state spaces. Such metrics provide a stable quantitative analogue of the notion of bisimulation for MDPs, and are suitable for use in MDP approximation. We show that the optimal value function associated with a discounted infinite horizon planning task varies continuously with respect to our metric distances.

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