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tf.contrib.opt.ShampooOptimizer

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The Shampoo Optimizer

Inherits From: 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.

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 for non-diagonal version of shampoo.
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

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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

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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

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get_slot

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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

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

See get_slot().

Returns
A list of strings.

minimize

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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

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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 Variables

  • GATE_GRAPH = 2
  • GATE_NONE = 0
  • GATE_OP = 1