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tfp.optimizer.StochasticGradientLangevinDynamics

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Class StochasticGradientLangevinDynamics

An optimizer module for stochastic gradient Langevin dynamics.

This implements the preconditioned Stochastic Gradient Langevin Dynamics optimizer [(Li et al., 2016)][1]. The optimization variable is regarded as a sample from the posterior under Stochastic Gradient Langevin Dynamics with noise rescaled in each dimension according to RMSProp.

Examples

Optimizing energy of a 3D-Gaussian distribution

This example demonstrates that for a fixed step size SGLD works as an approximate version of MALA (tfp.mcmc.MetropolisAdjustedLangevinAlgorithm).

import tensorflow as tf
import tensorflow_probability as tfp
import numpy as np

tfd = tfp.distributions
dtype = np.float32

with tf.Session(graph=tf.Graph()) as sess:
  # Set up random seed for the optimizer
  tf.set_random_seed(42)
  true_mean = dtype([0, 0, 0])
  true_cov = dtype([[1, 0.25, 0.25], [0.25, 1, 0.25], [0.25, 0.25, 1]])
  # Loss is defined through the Cholesky decomposition
  chol = tf.linalg.cholesky(true_cov)

  var_1 = tf.Variable(name='var_1', initial_value=[1., 1.])
  var_2 = tf.Variable(name='var_2', initial_value=[1.])

  def loss_fn():
    var = tf.concat([var_1, var_2], axis=-1)
    loss_part = tf.linalg.cholesky_solve(chol, tf.expand_dims(var, -1))
    return tf.linalg.matvec(loss_part, var, transpose_a=True)

  # Set up the learning rate with a polynomial decay
  step = tf.Variable(0, dtype=tf.int64)
  starter_learning_rate = .3
  end_learning_rate = 1e-4
  decay_steps = 1e4
  learning_rate = tf.compat.v1.train.polynomial_decay(
      starter_learning_rate,
      step,
      decay_steps,
      end_learning_rate,
      power=1.)

  # Set up the optimizer
  optimizer_kernel = tfp.optimizer.StochasticGradientLangevinDynamics(
      learning_rate=learning_rate, preconditioner_decay_rate=0.99)
  optimizer_kernel.iterations = step
  optimizer = optimizer_kernel.minimize(loss_fn, var_list=[var_1, var_2])

  # Number of training steps
  training_steps = 5000
  # Record the steps as and treat them as samples
  samples = [np.zeros([training_steps, 2]), np.zeros([training_steps, 1])]
  sess.run(tf.compat.v1.global_variables_initializer())
  for step in range(training_steps):
    sess.run(optimizer)
    sample = [sess.run(var_1), sess.run(var_2)]
    samples[0][step, :] = sample[0]
    samples[1][step, :] = sample[1]

  samples_ = np.concatenate(samples, axis=-1)
  sample_mean = np.mean(samples_, 0)
  print('sample mean', sample_mean)

Args: learning_rate: Scalar float-like Tensor. The base learning rate for the optimizer. Must be tuned to the specific function being minimized. preconditioner_decay_rate: Scalar float-like Tensor. The exponential decay rate of the rescaling of the preconditioner (RMSprop). (This is "alpha" in Li et al. (2016)). Should be smaller than but nearly 1 to approximate sampling from the posterior. (Default: 0.95) data_size: Scalar int-like Tensor. The effective number of points in the data set. Assumes that the loss is taken as the mean over a minibatch. Otherwise if the sum was taken, divide this number by the batch size. If a prior is included in the loss function, it should be normalized by data_size. Default value: 1. burnin: Scalar int-like Tensor. The number of iterations to collect gradient statistics to update the preconditioner before starting to draw noisy samples. (Default: 25) diagonal_bias: Scalar float-like Tensor. Term added to the diagonal of the preconditioner to prevent the preconditioner from degenerating. (Default: 1e-8) name: Python str describing ops managed by this function. (Default: "StochasticGradientLangevinDynamics") parallel_iterations: the number of coordinates for which the gradients of the preconditioning matrix can be computed in parallel. Must be a positive integer.

Raises:

  • InvalidArgumentError: If preconditioner_decay_rate is a Tensor not in (0,1].
  • NotImplementedError: If eager execution is enabled.

References

[1]: Chunyuan Li, Changyou Chen, David Carlson, and Lawrence Carin. Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks. In Association for the Advancement of Artificial Intelligence, 2016. https://arxiv.org/abs/1512.07666

__init__

View source

__init__(
    learning_rate,
    preconditioner_decay_rate=0.95,
    data_size=1,
    burnin=25,
    diagonal_bias=1e-08,
    name=None,
    parallel_iterations=10
)

Create a new Optimizer.

This must be called by the constructors of subclasses. Note that Optimizer instances should not bind to a single graph, and so shouldn't keep Tensors as member variables. Generally you should be able to use the _set_hyper()/state.get_hyper() facility instead.

This class in stateful and thread-compatible.

Args:

  • name: A non-empty string. The name to use for accumulators created for the optimizer.
  • **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.

Raises:

  • ValueError: If name is malformed.
  • RuntimeError: If _create_slots has been overridden instead of _create_vars.

Properties

iterations

Variable. The number of training steps this Optimizer has run.

variable_scope

Variable scope of all calls to tf.get_variable.

weights

Returns variables of this Optimizer based on the order created.

Methods

add_slot

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

Add a new slot variable for var.

add_weight

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

apply_gradients

apply_gradients(
    grads_and_vars,
    name=None
)

Apply gradients to variables.

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

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.

Returns:

An Operation that applies the specified gradients. If global_step was not None, that operation also increments global_step.

Raises:

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

from_config

from_config(
    cls,
    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

View source

get_config()

Returns the config of the optimimizer.

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

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

get_slot(
    var,
    slot_name
)

get_slot_names

get_slot_names()

A list of names for this optimizer's slots.

get_updates

get_updates(
    loss,
    params
)

get_weights

get_weights()

minimize

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. If global_step was not None, that operation also increments global_step.

Raises:

  • ValueError: If some of the variables are not Variable objects.

set_weights

set_weights(weights)

variables

variables()

Returns variables of this Optimizer based on the order created.