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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:

`ValueError` in case of any invalid argument.

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