tf.contrib.opt.ShampooOptimizer

The Shampoo Optimizer

Inherits From: Optimizer

tf.contrib.opt.ShampooOptimizer(
    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'
)

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.

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 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

View source

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

View source

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

View source

get_name()

get_slot

View source

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

View source

get_slot_names()

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

See get_slot().

Returns
A list of strings.

minimize

View source

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

View source

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 Variables

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