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# tfa.optimizers.ConditionalGradient

## Class ConditionalGradient

Optimizer that implements the Conditional Gradient optimization.

This optimizer helps handle constraints well.

Currently only supports frobenius norm constraint. See https://arxiv.org/pdf/1803.06453.pdf

variable -= (1-learning_rate) * (variable + lambda_ * gradient
/ (frobenius_norm(gradient) + epsilon))


Note that lambda_ here refers to the constraint "lambda" in the paper. epsilon is constant with tiny value as compared to the value of frobenius norm of gradient. The purpose of epsilon here is to avoid the case that the value of frobenius norm of gradient is 0.

In this implementation, epsilon defaults to $10^{-7}$.

## __init__

View source

__init__(
learning_rate,
lambda_,
epsilon=1e-07,
use_locking=False,
name='ConditionalGradient',
**kwargs
)


Construct a new conditional gradient optimizer.

#### Args:

• learning_rate: A Tensor or a floating point value. or a schedule that is a tf.keras.optimizers.schedules.LearningRateSchedule The learning rate.
• lambda_: A Tensor or a floating point value. The constraint.
• epsilon: A Tensor or a floating point value. A small constant for numerical stability when handling the case of norm of gradient to be zero.
• use_locking: If True, use locks for update operations.
• name: Optional name prefix for the operations created when applying gradients. Defaults to 'ConditionalGradient'.
• **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.

## Properties

### iterations

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

### 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. The iterations will be automatically increased by 1.

#### Raises:

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

### from_config

@classmethod
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. The iterations will be automatically increased by 1.

#### 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.