## Class NadamOptimizer

Inherits From: AdamOptimizer

Optimizer that implements the Nadam algorithm.

See Dozat, T., 2015.

## Methods

### __init__

__init__(
learning_rate=0.001,
beta1=0.9,
beta2=0.999,
epsilon=1e-08,
use_locking=False,
)


Initialization:

m_0 <- 0 (Initialize initial 1st moment vector)
v_0 <- 0 (Initialize initial 2nd moment vector)
t <- 0 (Initialize timestep)


The update rule for variable with gradient g uses an optimization described at the end of section2 of the paper:

t <- t + 1
lr_t <- learning_rate * sqrt(1 - beta2^t) / (1 - beta1^t)

m_t <- beta1 * m_{t-1} + (1 - beta1) * g
v_t <- beta2 * v_{t-1} + (1 - beta2) * g * g
variable <- variable - lr_t * m_t / (sqrt(v_t) + epsilon)


The default value of 1e-8 for epsilon might not be a good default in general. For example, when training an Inception network on ImageNet a current good choice is 1.0 or 0.1. Note that since AdamOptimizer uses the formulation just before Section 2.1 of the Kingma and Ba paper rather than the formulation in Algorithm 1, the "epsilon" referred to here is "epsilon hat" in the paper.

The sparse implementation of this algorithm (used when the gradient is an IndexedSlices object, typically because of tf.gather or an embedding lookup in the forward pass) does apply momentum to variable slices even if they were not used in the forward pass (meaning they have a gradient equal to zero). Momentum decay (beta1) is also applied to the entire momentum accumulator. This means that the sparse behavior is equivalent to the dense behavior (in contrast to some momentum implementations which ignore momentum unless a variable slice was actually used).

#### Args:

• learning_rate: A Tensor or a floating point value. The learning rate.
• beta1: A float value or a constant float tensor. The exponential decay rate for the 1st moment estimates.
• beta2: A float value or a constant float tensor. The exponential decay rate for the 2nd moment estimates.
• epsilon: A small constant for numerical stability. This epsilon is "epsilon hat" in the Kingma and Ba paper (in the formula just before Section 2.1), not the epsilon in Algorithm 1 of the paper.
• use_locking: If True use locks for update operations.
• name: Optional name for the operations created when applying gradients. Defaults to "Adam".

### apply_gradients

apply_gradients(
global_step=None,
name=None
)


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,
aggregation_method=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,
aggregation_method=None,
name=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 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, 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.