tf.contrib.opt.GGTOptimizer

Class `GGTOptimizer`

Inherits From: OptimizerV2

Defined in tensorflow/contrib/opt/python/training/ggt.py.

Optimizer that implements the GGT algorithm.

GGT has an advantage over sgd and adam on large models with poor conditioning, for example language models and CNNs, see [ABCHSZZ 2018].

`init`

__init__(
    learning_rate=0.001,
    beta1=0.9,
    use_locking=False,
    name='GGT',
    window=10,
    eps=0.0001,
    svd_eps=1e-06,
    sigma_eps=0.01
)

Construct a new GGT optimizer.

Initialization:

t <- 0 (Initialize timestep)
grad_buffer <- 0 (Initialize buffer for keeping past gradients)
flat_grad <- 0 (Initialize flattened gradient that contains gradients of all
                variables)
m_0 <- 0 (Initialize 1st moment vector)

Suppose all variables and their gradients are concatenated into vectors flat_vars and flat_grad. The update rule for flat_vars uses an optimization described at the beginning of section 2 of the paper:

t <- t + 1

m_t <- beta1 * m_{t-1} + (1 - beta1) * flat_grad
grad_buffer[(t-1) % window, :] <- m_t

M <- grad_buffer^T / sqrt(min(t, window))
U, sigma, _ <- SVD(M^TM + I * svd_eps)

sigma_sqrt_inv <- (sqrt(sigma) + sigma_eps)^(-3)
sigma_sqrt_min <- min(sqrt(sigma))

if sigma_sqrt_min > eps:
  new_step <- M U diag(sigma_sqrt_inv) U^T M^T m_t +
              (m_t - M U diag(1/sigma) U^T M^T m_t) / sigma_sqrt_min
else:
  new_step <- M U diag(sigma_sqrt_inv) U^T M^T m_t

flat_vars <- flat_vars - learning_rate * new_step

GGT provides the power of full-matrix adaptive regularization at a cost not much larger than SGD. As a result it is suited for large models where the gradient covariance matrix has a poor condition number that slows down first order methods. GGT uses the preconditioner from full-matrix AdaGrad, with gradient history attenuated exponentially as in Adam, and truncated to a window parameter. It has provable guarantees even for non-convex optimization that is never significantly worse than SGD and in some cases better.

Args:

learning_rate: A float hyperparameter. The learning rate.
beta1: A float hyperparameter. The exponential decay rate for the 1st moment estimates.
use_locking: If True use locks for update operations.
name: Optional name for the operations created when applying gradients. Defaults to "GGT".
window: An integer hyperparameter. The number of first moments to keep in computing the adaptive preconditioner.
eps: A float hyperparameter. Used to truncate small eigenvalues of the gradient covariance matrix.
svd_eps: A float hyperparameter. Used to stabilize SVD.
sigma_eps: A float hyperparameter. Used to regularize matrix inversion.

Methods

`tf.contrib.opt.GGTOptimizer.apply_gradients`

apply_gradients(
    grads_and_vars,
    global_step=None,
    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 as returned by compute_gradients().
global_step: Optional Variable to increment by one after the variables have been updated.
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.

`tf.contrib.opt.GGTOptimizer.compute_gradients`

compute_gradients(
    loss,
    var_list=None,
    gate_gradients=GATE_OP,
    aggregation_method=None,
    grad_loss=None,
    stop_gradients=None,
    scale_loss_by_num_replicas=None
)

Compute gradients of loss for the variables in var_list.

This is the first part of minimize(). It returns a list of (gradient, variable) pairs where "gradient" is the gradient for "variable". Note that "gradient" can be a Tensor, an IndexedSlices, or None if there is no gradient for the given variable.

Args:

loss: A Tensor containing the value to minimize or a callable taking no arguments which returns the value to minimize. When eager execution is enabled it must be a callable.
var_list: Optional list or tuple of tf.Variable to update to minimize loss. Defaults to the list of variables collected in the graph under the key GraphKeys.TRAINABLE_VARIABLES.
gate_gradients: How to gate the computation of gradients. Can be GATE_NONE, GATE_OP, or GATE_GRAPH.
aggregation_method: Specifies the method used to combine gradient terms. Valid values are defined in the class AggregationMethod.
grad_loss: Optional. A Tensor holding the gradient computed for loss.
stop_gradients: Optional. A Tensor or list of tensors not to differentiate through.
scale_loss_by_num_replicas: Optional boolean. If true, scale the loss down by the number of replicas. By default, auto-detects whether this is needed.

Returns:

A list of (gradient, variable) pairs. Variable is always present, but gradient can be None.

Raises:

TypeError: If var_list contains anything else than Variable objects.
ValueError: If some arguments are invalid.
RuntimeError: If called with eager execution enabled and loss is not callable.

Eager Compatibility

When eager execution is enabled, gate_gradients, and aggregation_method are ignored.

`tf.contrib.opt.GGTOptimizer.get_name`

get_name()

`tf.contrib.opt.GGTOptimizer.get_slot`

get_slot(
    var,
    name
)

Return a slot named name created for var by the Optimizer.

Some Optimizer subclasses use additional variables. For example Momentum and Adagrad use variables to accumulate updates. This method gives access to these Variable objects if for some reason you need them.

Use get_slot_names() to get the list of slot names created by the Optimizer.

Args:

var: A variable passed to minimize() or apply_gradients().
name: A string.

Returns:

The Variable for the slot if it was created, None otherwise.

`tf.contrib.opt.GGTOptimizer.get_slot_names`

get_slot_names()

Return a list of the names of slots created by the Optimizer.

See get_slot().

Returns:

A list of strings.

`tf.contrib.opt.GGTOptimizer.minimize`

minimize(
    loss,
    global_step=None,
    var_list=None,
    gate_gradients=GATE_OP,
    aggregation_method=None,
    name=None,
    grad_loss=None,
    stop_gradients=None,
    scale_loss_by_num_replicas=None
)

Add operations to minimize loss by updating var_list.

This method simply combines calls compute_gradients() and apply_gradients(). If you want to process the gradient before applying them call compute_gradients() and apply_gradients() explicitly instead of using this function.

Args:

loss: A Tensor containing the value to minimize.
global_step: Optional Variable to increment by one after the variables have been updated.
var_list: Optional list or tuple of Variable objects to update to minimize loss. Defaults to the list of variables collected in the graph under the key GraphKeys.TRAINABLE_VARIABLES.
gate_gradients: How to gate the computation of gradients. Can be GATE_NONE, GATE_OP, or GATE_GRAPH.
aggregation_method: Specifies the method used to combine gradient terms. Valid values are defined in the class AggregationMethod.
name: Optional name for the returned operation.
grad_loss: Optional. A Tensor holding the gradient computed for loss.
stop_gradients: Optional. A Tensor or list of tensors not to differentiate through.
scale_loss_by_num_replicas: Optional boolean. If true, scale the loss down by the number of replicas. By default, auto-detects whether this is needed.

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.

Eager Compatibility

When eager execution is enabled, loss should be a Python function that takes elements of var_list as arguments and computes the value to be minimized. If var_list is None, loss should take no arguments. Minimization (and gradient computation) is done with respect to the elements of var_list if not None, else with respect to any trainable variables created during the execution of the loss function. gate_gradients, aggregation_method, and grad_loss are ignored when eager execution is enabled.

`tf.contrib.opt.GGTOptimizer.variables`

variables()

A list of variables which encode the current state of Optimizer.

Includes slot variables and additional global variables created by the optimizer in the current default graph.

Returns:

A list of variables.

tf.contrib.opt.GGTOptimizer

Class `GGTOptimizer`

`init`

Args:

Methods

`tf.contrib.opt.GGTOptimizer.apply_gradients`

Args:

Returns:

Raises:

`tf.contrib.opt.GGTOptimizer.compute_gradients`

Args:

Returns:

Raises:

Eager Compatibility

`tf.contrib.opt.GGTOptimizer.get_name`

`tf.contrib.opt.GGTOptimizer.get_slot`

Args:

Returns:

`tf.contrib.opt.GGTOptimizer.get_slot_names`

Returns:

`tf.contrib.opt.GGTOptimizer.minimize`

Args:

Returns:

Raises:

Eager Compatibility

`tf.contrib.opt.GGTOptimizer.variables`

Returns:

Class Members

`GATE_GRAPH`

`GATE_NONE`

`GATE_OP`

tf.contrib.opt.GGTOptimizer

Class GGTOptimizer

__init__

Args:

Methods

tf.contrib.opt.GGTOptimizer.apply_gradients

Args:

Returns:

Raises:

tf.contrib.opt.GGTOptimizer.compute_gradients

Args:

Returns:

Raises:

Eager Compatibility

tf.contrib.opt.GGTOptimizer.get_name

tf.contrib.opt.GGTOptimizer.get_slot

Args:

Returns:

tf.contrib.opt.GGTOptimizer.get_slot_names

Returns:

tf.contrib.opt.GGTOptimizer.minimize

Args:

Returns:

Raises:

Eager Compatibility

tf.contrib.opt.GGTOptimizer.variables

Returns:

Class Members

GATE_GRAPH

GATE_NONE

GATE_OP

Class `GGTOptimizer`

`init`

`tf.contrib.opt.GGTOptimizer.apply_gradients`

`tf.contrib.opt.GGTOptimizer.compute_gradients`

`tf.contrib.opt.GGTOptimizer.get_name`

`tf.contrib.opt.GGTOptimizer.get_slot`

`tf.contrib.opt.GGTOptimizer.get_slot_names`

`tf.contrib.opt.GGTOptimizer.minimize`

`tf.contrib.opt.GGTOptimizer.variables`

`GATE_GRAPH`

`GATE_NONE`

`GATE_OP`