tf.contrib.opt.ShampooOptimizer

Class ShampooOptimizer

Inherits From: Optimizer

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

The Shampoo Optimizer

Variant of Adagrad using one preconditioner matrix per variable dimension. For details, see https://arxiv.org/abs/1802.09568

gbar is time-weighted accumulated gradient: gbar[t] = gbar_decay[t] * gbar[t-1] + gbar_weight[t] * g[t]

mat_gbar is time-weighted accumulated gradient square: mat_gbar_j[t] = mat_gbar_decay[t] * mat_gbar_j[t-1] + mat_gbar_weight[t] * gg_j[t] where if g[t] = g_abcd then gg_a[t] = g_abcd g_a'bcd (Einstein notation)

Update rule: w[t+1] = w[t] - learning_rate[t] * Prod_j mat_gbar_j[t]^(-alpha/n) gbar[t] Again, mat_gbar_j[t]^(-alpha) gbar[t] is a tensor contraction along the j'th dimension of gbar[t] with the first dimension of mat_gbar_j[t]^(-alpha/n), where alpha is a hyperparameter, and n = rank of the variable. Prod_j represents doing this contraction for all j in 0..n-1.

Typically learning_rate is constant, but could be time dependent by passing a lambda function that depends on step.

__init__

__init__(
    global_step=0,
    max_matrix_size=768,
    gbar_decay=0.0,
    gbar_weight=1.0,
    mat_gbar_decay=1.0,
    mat_gbar_weight=1.0,
    learning_rate=1.0,
    svd_interval=1,
    precond_update_interval=1,
    epsilon=0.0001,
    alpha=0.5,
    use_iterative_root=False,
    use_locking=False,
    name='Shampoo'
)

Default values of the various hyper-parameters.

gbar_decay, gbar_weight etc. can be a float or a time varying parameter. For time-varying parameters use e.g. "lambda T: T / (T + 1.0)" where the expression in the lambda is a tensorflow expression

Args:

  • global_step: tensorflow variable indicating the step.
  • max_matrix_size: We do not perform SVD for matrices larger than this.
  • gbar_decay: * gbar_weight: Used to update gbar: gbar[t] = gbar_decay[t] * gbar[t-1] + gbar_weight[t] * g[t]
  • mat_gbar_decay: * mat_gbar_weight: Used to update mat_gbar: mat_gbar_j[t] = mat_gbar_decay[t] * mat_gbar_j[t-1] + mat_gbar_weight[t] * gg_j[t]
  • learning_rate: Similar to SGD
  • svd_interval: We should do SVD after this many steps. Default = 1, i.e. every step. Usually 20 leads to no loss of accuracy, and 50 or 100 is also OK. May also want more often early, and less often later - set in caller as for example: "svd_interval = lambda(T): tf.cond( T < 2000, lambda: 20.0, lambda: 1000.0)"
  • precond_update_interval: We should update the preconditioners after this many steps. Default = 1. Usually less than svd_interval.
  • epsilon: epsilon * I_n is added to each mat_gbar_j for stability
  • alpha: total power of the preconditioners.
  • use_iterative_root: should the optimizer use SVD (faster) or the iterative root method (for TPU) for finding the roots of PSD matrices.
  • use_locking: * name: name of optimizer.

Methods

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.
  • RuntimeError: If you should use _distributed_apply() instead.

compute_gradients

compute_gradients(
    loss,
    var_list=None,
    gate_gradients=GATE_OP,
    aggregation_method=None,
    colocate_gradients_with_ops=False,
    grad_loss=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.
  • colocate_gradients_with_ops: If True, try colocating gradients with the corresponding op.
  • grad_loss: Optional. A Tensor holding the gradient computed for loss.

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, aggregation_method, and colocate_gradients_with_ops are ignored.

get_name

get_name()

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.

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.

minimize

minimize(
    loss,
    global_step=None,
    var_list=None,
    gate_gradients=GATE_OP,
    aggregation_method=None,
    colocate_gradients_with_ops=False,
    name=None,
    grad_loss=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.
  • colocate_gradients_with_ops: If True, try colocating gradients with the corresponding op.
  • name: Optional name for the returned operation.
  • grad_loss: Optional. A Tensor holding the gradient computed for loss.

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 no arguments and computes the value to be minimized. 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, colocate_gradients_with_ops and grad_loss are ignored when eager execution is enabled.

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.

Class Members

GATE_GRAPH

GATE_NONE

GATE_OP