tf.keras.optimizers.RMSprop

TensorFlow 1 version View source on GitHub

Optimizer that implements the RMSprop algorithm.

Inherits From: Optimizer

tf.keras.optimizers.RMSprop(
    learning_rate=0.001, rho=0.9, momentum=0.0, epsilon=1e-07, centered=False,
    name='RMSprop', **kwargs
)

A detailed description of rmsprop.

  • maintain a moving (discounted) average of the square of gradients
  • divide gradient by the root of this average

The default settings does not use momentum:

$$rms_t = \rho * rms_{t-1} + (1-\rho) * g_t^2$$
$$\theta_t = \theta_{t-1} - \mathrm{learning\_rate} * g_t / \sqrt{rms_t + \epsilon}$$

Since $x/x^2 = sign(x)$, this is an smoothed approximation of:

$$ \theta_t = \theta_{t-1} - \mathrm{learning\_rate} * sign(g_t) $$

With momentum the update is:

$$rms_t = \rho * rms_{t-1} + (1-\rho) * g_t^2$$
$$mom_t = \mathrm{momentum} * mom_{t-1} + g_t / \sqrt{rms_t + \epsilon}$$
$$\theta_t = \theta_{t-1} - \mathrm{learning\_rate} * mom_t$$

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:

$$mg_t = \rho * mg_{t-1} + (1-\rho) * g_t$$
$$rms_t = \rho * rms_{t-1} + (1-\rho) * g_t^2$$
$$mom_t = \mathrm{momentum} * mom_{t-1} + \mathrm{learning\_rate} * g_t / sqrt(rms_t - mg_t^2 + \epsilon)$$
$$\theta_t = \theta_{t-1} - mom_t$$

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

References See ([pdf] http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf).

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. Defeaults 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". @compatibility(eager) When eager execution is enabled, learning_rate, decay, momentum, and epsilon can each be a callable that takes no arguments and returns the actual value to use. This can be useful for changing these values across different invocations of optimizer functions. @end_compatibility
**kwargs keyword arguments. Allowed to be {clipnorm, clipvalue, lr, decay}. clipnorm is clip gradients by norm; clipvalue is clip gradients by value, decay is included for backward compatibility to allow time inverse decay of learning rate. lr is included for backward compatibility, recommended to use learning_rate instead.

iterations Variable. The number of training steps this Optimizer has run.
weights Returns variables of this Optimizer based on the order created.

Methods

add_slot

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add_slot(
    var, slot_name, initializer='zeros'
)

Add a new slot variable for var.

add_weight

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add_weight(
    name, shape, dtype=None, initializer='zeros', trainable=None,
    synchronization=tf.VariableSynchronization.AUTO,
    aggregation=tf.compat.v1.VariableAggregation.NONE
)

apply_gradients

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apply_gradients(
    grads_and_vars, name=None, experimental_aggregate_gradients=True
)

Apply gradients to variables.

This is the second part of minimize(). It returns an Operation that applies gradients.

The method sums gradients from all replicas in the presence of tf.distribute.Strategy by default. You can aggregate gradients yourself by passing experimental_aggregate_gradients=False.

Example:

grads = tape.gradient(loss, vars)
grads = tf.distribute.get_replica_context().all_reduce('sum', grads)
# Processing aggregated gradients.
optimizer.apply_gradients(zip(grads, vars),
    experimental_aggregate_gradients=False)

Args
grads_and_vars List of (gradient, variable) pairs.
name Optional name for the returned operation. Default to the name passed to the Optimizer constructor.
experimental_aggregate_gradients Whether to sum gradients from different replicas in the presense of tf.distribute.Strategy. If False, it's user responsibility to aggregate the gradients. Default to True.

Returns
An Operation that applies the specified gradients. The iterations will be automatically increased by 1.

Raises
TypeError If grads_and_vars is malformed.
ValueError If none of the variables have gradients.

from_config

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@classmethod
from_config(
    config, custom_objects=None
)

Creates an optimizer from its config.

This method is the reverse of get_config, capable of instantiating the same optimizer from the config dictionary.

Arguments
config A Python dictionary, typically the output of get_config.
custom_objects A Python dictionary mapping names to additional Python objects used to create this optimizer, such as a function used for a hyperparameter.

Returns
An optimizer instance.

get_config

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get_config()

Returns the config of the optimizer.

An optimizer config is a Python dictionary (serializable) containing the configuration of an optimizer. The same optimizer can be reinstantiated later (without any saved state) from this configuration.

Returns
Python dictionary.

get_gradients

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get_gradients(
    loss, params
)

Returns gradients of loss with respect to params.

Arguments
loss Loss tensor.
params List of variables.

Returns
List of gradient tensors.

Raises
ValueError In case any gradient cannot be computed (e.g. if gradient function not implemented).

get_slot

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get_slot(
    var, slot_name
)

get_slot_names

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get_slot_names()

A list of names for this optimizer's slots.

get_updates

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get_updates(
    loss, params
)

get_weights

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get_weights()

Returns the current weights of the optimizer.

The weights of an optimizer are its state (ie, variables). This function returns the weight values associated with this optimizer as a list of Numpy arrays. The first value is always the iterations count of the optimizer, followed by the optimizer's state variables in the order they were created. The returned list can in turn be used to load state into similarly parameterized optimizers.

For example, the RMSprop optimizer for this simple model returns a list of three values-- the iteration count, followed by the root-mean-square value of the kernel and bias of the single Dense layer:

opt = tf.keras.optimizers.RMSprop()
m = tf.keras.models.Sequential([tf.keras.layers.Dense(10)])
m.compile(opt, loss='mse')
data = np.arange(100).reshape(5, 20)
labels = np.zeros(5)
print('Training'); results = m.fit(data, labels)
Training ...
len(opt.get_weights())
3

Returns
Weights values as a list of numpy arrays.

minimize

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minimize(
    loss, var_list, grad_loss=None, name=None
)

Minimize loss by updating var_list.

This method simply computes gradient using tf.GradientTape and calls apply_gradients(). If you want to process the gradient before applying then call tf.GradientTape and apply_gradients() explicitly instead of using this function.

Args
loss A callable taking no arguments which returns the value to minimize.
var_list list or tuple of Variable objects to update to minimize loss, or a callable returning the list or tuple of Variable objects. Use callable when the variable list would otherwise be incomplete before minimize since the variables are created at the first time loss is called.
grad_loss Optional. A Tensor holding the gradient computed for loss.
name Optional name for the returned operation.

Returns
An Operation that updates the variables in var_list. The iterations will be automatically increased by 1.

Raises
ValueError If some of the variables are not Variable objects.

set_weights

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set_weights(
    weights
)

Set the weights of the optimizer.

The weights of an optimizer are its state (ie, variables). This function takes the weight values associated with this optimizer as a list of Numpy arrays. The first value is always the iterations count of the optimizer, followed by the optimizer's state variables in the order they are created. The passed values are used to set the new state of the optimizer.

For example, the RMSprop optimizer for this simple model takes a list of three values-- the iteration count, followed by the root-mean-square value of the kernel and bias of the single Dense layer:

opt = tf.keras.optimizers.RMSprop()
m = tf.keras.models.Sequential([tf.keras.layers.Dense(10)])
m.compile(opt, loss='mse')
data = np.arange(100).reshape(5, 20)
labels = np.zeros(5)
print('Training'); results = m.fit(data, labels)
Training ...
new_weights = [np.array(10), np.ones([20, 10]), np.zeros([10])]
opt.set_weights(new_weights)
opt.iterations
<tf.Variable 'RMSprop/iter:0' shape=() dtype=int64, numpy=10>

Arguments
weights weight values as a list of numpy arrays.

variables

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variables()

Returns variables of this Optimizer based on the order created.