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Arguments
learning_rate: Initial value for the learning rate: either a floating point value, or a tf.keras.optimizers.schedules.LearningRateSchedule instance. Defaults to 0.001. Note that Adadelta tends to benefit from higher initial learning rate values compared to other optimizers. To match the exact form in the original paper, use 1.0.
rho: A Tensor or a floating point value. The decay rate.
epsilon: Small floating point value used to maintain numerical stability.
name: Optional name prefix for the operations created when applying gradients. Defaults to "Adadelta".
**kwargs: Keyword arguments. Allowed to be one of "clipnorm" or "clipvalue". "clipnorm" (float) clips gradients by norm and represents the maximum norm of each parameter; "clipvalue" (float) clips gradient by value and represents the maximum absolute value of each parameter.
Reference
Zeiler, 2012Adam
Adam class
tf.keras.optimizers.Adam(
learning_rate=0.001,
beta_1=0.9,
beta_2=0.999,
epsilon=1e-07,
amsgrad=False,
name="Adam",
**kwargs
)
Optimizer that implements the Adam algorithm.
Adam optimization is a stochastic gradient descent method that is based on adaptive estimation of first-order and second-order moments.
According to Kingma et al., 2014, the method is "computationally efficient, has little memory requirement, invariant to diagonal rescaling of gradients, and is well suited for problems that are large in terms of data/parameters".
Arguments
learning_rate: A Tensor, floating point value, or a schedule that is a tf.keras.optimizers.schedules.LearningRateSchedule, or a callable that takes no arguments and returns the actual value to use, The learning rate. Defaults to 0.001.
beta_1: A float value or a constant float tensor, or a callable that takes no arguments and returns the actual value to use. The exponential decay rate for the 1st moment estimates. Defaults to 0.9.
beta_2: A float value or a constant float tensor, or a callable that takes no arguments and returns the actual value to use, The exponential decay rate for the 2nd moment estimates. Defaults to 0.999.
epsilon: A small constant for numerical stability. This epsilon is "epsilon hat" in the Kingma and Ba paper (in the formula just before Section 2.1), not the epsilon in Algorithm 1 of the paper. Defaults to 1e-7.
amsgrad: Boolean. Whether to apply AMSGrad variant of this algorithm from the paper "On the Convergence of Adam and beyond". Defaults to False.
name: Optional name for the operations created when applying gradients. Defaults to "Adam".
**kwargs: Keyword arguments. Allowed to be one of "clipnorm" or "clipvalue". "clipnorm" (float) clips gradients by norm; "clipvalue" (float) clips gradients by value.
Usage:
>>> opt = tf.keras.optimizers.Adam(learning_rate=0.1)
>>> var1 = tf.Variable(10.0)
>>> loss = lambda: (var1 ** 2)/2.0 # d(loss)/d(var1) == var1
>>> step_count = opt.minimize(loss, [var1]).numpy()
>>> # The first step is `-learning_rate*sign(grad)`
>>> var1.numpy()
9.9
Reference
Kingma et al., 2014
Reddi et al., 2018 for amsgrad.
Notes:
The default value of 1e-7 for epsilon might not be a good default in general. For example, when training an Inception network on ImageNet a current good choice is 1.0 or 0.1. Note that since Adam uses the formulation just before Section 2.1 of the Kingma and Ba paper rather than the formulation in Algorithm 1, the "epsilon" referred to here is "epsilon hat" in the paper.
The sparse implementation of this algorithm (used when the gradient is an IndexedSlices object, typically because of tf.gather or an embedding lookup in the forward pass) does apply momentum to variable slices even if they were not used in the forward pass (meaning they have a gradient equal to zero). Momentum decay (beta1) is also applied to the entire momentum accumulator. This means that the sparse behavior is equivalent to the dense behavior (in contrast to some momentum implementations which ignore momentum unless a variable slice was actually used).
RMSprop
RMSprop class
tf.keras.optimizers.RMSprop(
learning_rate=0.001,
rho=0.9,
momentum=0.0,
epsilon=1e-07,
centered=False,
name="RMSprop",
**kwargs
)
Optimizer that implements the RMSprop algorithm.
The gist of RMSprop is to:
Maintain a moving (discounted) average of the square of gradients
Divide the gradient by the root of this average
This implementation of RMSprop uses plain momentum, not Nesterov momentum.
The centered version additionally maintains a moving average of the gradients, and uses that average to estimate the variance.
Arguments
learning_rate: A Tensor, floating point value, or a schedule that is a tf.keras.optimizers.schedules.LearningRateSchedule, or a callable that takes no arguments and returns the actual value to use. The learning rate. Defaults to 0.001.
rho: Discounting factor for the history/coming gradient. Defaults to 0.9.
momentum: A scalar or a scalar Tensor. Defaults to 0.0.
epsilon: A small constant for numerical stability. This epsilon is "epsilon hat" in the Kingma and Ba paper (in the formula just before Section 2.1), not the epsilon in Algorithm 1 of the paper. Defaults to 1e-7.
centered: Boolean. If True, gradients are normalized by the estimated variance of the gradient; if False, by the uncentered second moment. Setting this to True may help with training, but is slightly more expensive in terms of computation and memory. Defaults to False.
name: Optional name prefix for the operations created when applying gradients. Defaults to "RMSprop".
**kwargs: Keyword arguments. Allowed to be one of "clipnorm" or "clipvalue". "clipnorm" (float) clips gradients by norm; "clipvalue" (float) clips gradients by value.
Note that in the dense implementation of this algorithm, variables and their corresponding accumulators (momentum, gradient moving average, square gradient moving average) will be updated even if the gradient is zero (i.e. accumulators will decay, momentum will be applied). The sparse implementation (used when the gradient is an IndexedSlices object, typically because of tf.gather or an embedding lookup in the forward pass) will not update variable slices or their accumulators unless those slices were used in the forward pass (nor is there an "eventual" correction to account for these omitted updates). This leads to more efficient updates for large embedding lookup tables (where most of the slices are not accessed in a particular graph execution), but differs from the published algorithm.
Usage:
>>> opt = tf.keras.optimizers.RMSprop(learning_rate=0.1)
>>> var1 = tf.Variable(10.0)
>>> loss = lambda: (var1 ** 2) / 2.0 # d(loss) / d(var1) = var1
>>> step_count = opt.minimize(loss, [var1]).numpy()
>>> var1.numpy()
9.683772
Reference