Adamax, a variant of Adam based on the infinity norm, is a first-order gradient-based optimization method. Due to its capability of adjusting the learning rate based on data characteristics, it is suited to learn time-variant process, e.g., speech data with dynamically changed noise conditions. Default parameters follow those provided in the paper (see references below).

Initialization:

```
m <- 0 # Initialize initial 1st moment vector
u <- 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 (see the referenece section):

## Usage

```
optimizer_adamax(
learning_rate = 0.001,
beta_1 = 0.9,
beta_2 = 0.999,
epsilon = 1e-07,
weight_decay = NULL,
clipnorm = NULL,
clipvalue = NULL,
global_clipnorm = NULL,
use_ema = FALSE,
ema_momentum = 0.99,
ema_overwrite_frequency = NULL,
name = "adamax",
...,
loss_scale_factor = NULL,
gradient_accumulation_steps = NULL
)
```

## Arguments

- learning_rate
A float, a

`LearningRateSchedule()`

instance, or a callable that takes no arguments and returns the actual value to use. The learning rate. Defaults to`0.001`

.- 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: String. The name to use for momentum accumulator weights created by the optimizer.

- weight_decay
Float. If set, weight decay is applied.

- clipnorm
Float. If set, the gradient of each weight is individually clipped so that its norm is no higher than this value.

- clipvalue
Float. If set, the gradient of each weight is clipped to be no higher than this value.

- global_clipnorm
Float. If set, the gradient of all weights is clipped so that their global norm is no higher than this value.

- use_ema
Boolean, defaults to FALSE. If TRUE, exponential moving average (EMA) is applied. EMA consists of computing an exponential moving average of the weights of the model (as the weight values change after each training batch), and periodically overwriting the weights with their moving average.

- ema_momentum
Float, defaults to 0.99. Only used if

`use_ema=TRUE`

. This is the momentum to use when computing the EMA of the model's weights:`new_average = ema_momentum * old_average + (1 - ema_momentum) * current_variable_value`

.- ema_overwrite_frequency
Int or NULL, defaults to NULL. Only used if

`use_ema=TRUE`

. Every`ema_overwrite_frequency`

steps of iterations, we overwrite the model variable by its moving average. If NULL, the optimizer does not overwrite model variables in the middle of training, and you need to explicitly overwrite the variables at the end of training by calling`optimizer$finalize_variable_values()`

(which updates the model variables in-place). When using the built-in`fit()`

training loop, this happens automatically after the last epoch, and you don't need to do anything.- name
String, name for the object

- ...
For forward/backward compatability.

- loss_scale_factor
Float or

`NULL`

. If a float, the scale factor will be multiplied the loss before computing gradients, and the inverse of the scale factor will be multiplied by the gradients before updating variables. Useful for preventing underflow during mixed precision training. Alternately,`optimizer_loss_scale()`

will automatically set a loss scale factor.- gradient_accumulation_steps
Int or

`NULL`

. If an int, model & optimizer variables will not be updated at every step; instead they will be updated every`gradient_accumulation_steps`

steps, using the average value of the gradients since the last update. This is known as "gradient accumulation". This can be useful when your batch size is very small, in order to reduce gradient noise at each update step.