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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.

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.

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

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Add a new slot variable for var.

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### apply_gradients

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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

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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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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

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Returns gradients of loss with respect to params.

Arguments
loss Loss tensor.
params List of variables.

Returns

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

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### get_slot_names

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A list of names for this optimizer's slots.

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### minimize

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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.

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### variables

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Returns variables of this Optimizer based on the order created.

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