Optimizer that implements the NAdam algorithm.

Inherits From: Optimizer

#### Initialization:

$$m_0 := 0 \text{(Initialize 1st moment vector)}$$
$$v_0 := 0 \text{(Initialize 2nd moment vector)}$$
$$mu_0 := 1$$
$$t := 0 \text{(Initialize timestep)}$$

#### Computes:

$$t := t + 1$$
$$\mu_t := \beta_1 * (1 - 0.5 * 0.96^{0.004 * t})$$
$$g' := g / (1 - \prod_{i=1}^{t}{\mu_i})$$
$$m_t := \beta_1 * m_{t-1} + (1 - \beta_1) * g$$
$$m' := m_t / (1 - \prod_{i=1}^{t+1}{\mu_i})$$
$$v_t := \beta_2 * v_{t-1} + (1 - \beta_2) * g * g$$
$$v' := v_t / (1 - \beta_2^t)$$
$$\bar{m} := (1 - \mu_t) * g' + \mu_{t+1} * m'$$
$$\theta_t := \theta_{t-1} - lr * \bar{m} / (\sqrt{v'} + \epsilon)$$

gradient is evaluated at theta(t) + momentum * v(t), and the variables always store theta + beta_1 * m / sqrt(v) instead of theta.

References See Dozat, T., 2015.

## __init__

View source

__init__(
learning_rate=0.001,
beta_1=0.9,
beta_2=0.999,
epsilon=1e-07,
**kwargs
)

#### Args:

• learning_rate: A Tensor or a floating point value. The learning rate.
• beta_1: A float value or a constant float tensor. The exponential decay rate for the 1st moment estimates.
• beta_2: A float value or a constant float tensor. The exponential decay rate for the exponentially weighted infinity norm.
• epsilon: A small constant for numerical stability.
• name: Optional name for the operations created when applying gradients. Defaults to "Adamax".
• **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

View source

var,
slot_name,
initializer='zeros'
)

Add a new slot variable for var.

View source

name,
shape,
dtype=None,
initializer='zeros',
trainable=None,
synchronization=tf.VariableSynchronization.AUTO,
aggregation=tf.compat.v1.VariableAggregation.NONE
)

View source

name=None
)

This is the second part of minimize(). It returns an Operation that applies gradients.

#### Args:

• 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

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@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

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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.

View source

loss,
params
)

Returns gradients of loss with respect to params.

#### Arguments:

• loss: Loss tensor.
• params: List of variables.

#### Raises:

• ValueError: In case any gradient cannot be computed (e.g. if gradient function not implemented).

View source

get_slot(
var,
slot_name
)

### get_slot_names

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get_slot_names()

A list of names for this optimizer's slots.

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loss,
params
)

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get_weights()

### minimize

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minimize(
loss,
var_list,
name=None
)

Minimize loss by updating var_list.

#### 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.
• 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

View source

set_weights(weights)

### variables

View source

variables()

Returns variables of this Optimizer based on the order created.