Optimizer that implements the Adamax algorithm.

Inherits From: `Optimizer`

It is a variant of Adam based on the infinity norm. Default parameters follow those provided in the paper. Adamax is sometimes superior to adam, specially in models with embeddings.

#### Initialization:

``````m = 0  # Initialize initial 1st moment vector
v = 0  # Initialize the exponentially weighted infinity norm
t = 0  # Initialize timestep
``````

The update rule for parameter `w` with gradient `g` is described at the end of section 7.1 of the paper:

``````t += 1
m = beta1 * m + (1 - beta) * g
v = max(beta2 * v, abs(g))
current_lr = learning_rate / (1 - beta1 ** t)
w = w - current_lr * m / (v + epsilon)
``````

Similarly to `Adam`, the epsilon is added for numerical stability (especially to get rid of division by zero when `v_t == 0`).

In contrast to `Adam`, 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) only updates variable slices and corresponding `m_t`, `v_t` terms when that part of the variable was used in the forward pass. This means that the sparse behavior is contrast to the dense behavior (similar to some momentum implementations which ignore momentum unless a variable slice was actually used).

`learning_rate` A `Tensor`, floating point value, or a schedule that is a `tf.keras.optimizers.schedules.LearningRateSchedule`. 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 one of `"clipnorm"` or `"clipvalue"`. `"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips gradients by value.

#### Reference:

`name` A non-empty string. The name to use for accumulators created for the optimizer.
`**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.

`ValueError` If name is malformed.

`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`

View source

Add a new slot variable for `var`.

View source

### `apply_gradients`

View source

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

The method sums gradients from all replicas in the presence of `tf.distribute.Strategy` by default. You can aggregate gradients yourself by passing `experimental_aggregate_gradients=False`.

#### Example:

``````grads = tape.gradient(loss, vars)

``````

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.
`experimental_aggregate_gradients` Whether to sum gradients from different replicas in the presense of `tf.distribute.Strategy`. If False, it's user responsibility to aggregate the gradients. Default to True.

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`

View source

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

Returns the config of the optimizer.

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`

View source

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).

View source

### `get_slot_names`

View source

A list of names for this optimizer's slots.

View source

### `get_weights`

View source

Returns the current weights of the optimizer.

The weights of an optimizer are its state (ie, variables). This function returns the weight values associated with this optimizer as a list of Numpy arrays. The first value is always the iterations count of the optimizer, followed by the optimizer's state variables in the order they were created. The returned list can in turn be used to load state into similarly parameterized optimizers.

For example, the RMSprop optimizer for this simple model returns a list of three values-- the iteration count, followed by