# A `LearningRateSchedule`

that uses a polynomial decay schedule.

Source: `R/optimizers-schedules.R`

`learning_rate_schedule_polynomial_decay.Rd`

It is commonly observed that a monotonically decreasing learning rate, whose
degree of change is carefully chosen, results in a better performing model.
This schedule applies a polynomial decay function to an optimizer step,
given a provided `initial_learning_rate`

, to reach an `end_learning_rate`

in the given `decay_steps`

.

It requires a `step`

value to compute the decayed learning rate. You
can just pass a backend variable that you increment at each training
step.

The schedule is a 1-arg callable that produces a decayed learning rate when passed the current optimizer step. This can be useful for changing the learning rate value across different invocations of optimizer functions. It is computed as:

```
decayed_learning_rate <- function(step) {
step = min(step, decay_steps)
((initial_learning_rate - end_learning_rate) *
(1 - step / decay_steps) ^ (power)) +
end_learning_rate
}
```

If `cycle`

is TRUE then a multiple of `decay_steps`

is used, the first one
that is bigger than `step`

.

```
decayed_learning_rate <- function(step) {
decay_steps = decay_steps * ceil(step / decay_steps)
((initial_learning_rate - end_learning_rate) *
(1 - step / decay_steps) ^ (power)) +
end_learning_rate
}
```

You can pass this schedule directly into a `Optimizer`

as the learning rate.

## Usage

```
learning_rate_schedule_polynomial_decay(
initial_learning_rate,
decay_steps,
end_learning_rate = 1e-04,
power = 1,
cycle = FALSE,
name = "PolynomialDecay"
)
```

## Arguments

- initial_learning_rate
A float. The initial learning rate.

- decay_steps
A integer. Must be positive. See the decay computation above.

- end_learning_rate
A float. The minimal end learning rate.

- power
A float. The power of the polynomial. Defaults to

`1.0`

.- cycle
A boolean, whether it should cycle beyond decay_steps.

- name
String. Optional name of the operation. Defaults to

`"PolynomialDecay"`

.

## Value

A 1-arg callable learning rate schedule that takes the current optimizer
step and outputs the decayed learning rate, a scalar tensor of the
same type as `initial_learning_rate`

.

## Examples

Fit a model while decaying from 0.1 to 0.01 in 10000 steps using sqrt (i.e. power=0.5):

```
...
starter_learning_rate <- 0.1
end_learning_rate <- 0.01
decay_steps <- 10000
learning_rate_fn <- learning_rate_schedule_polynomial_decay(
starter_learning_rate,
decay_steps,
end_learning_rate,
power=0.5)
model %>% compile(
optimizer = optimizer_sgd(learning_rate=learning_rate_fn),
loss = 'sparse_categorical_crossentropy',
metrics = 'accuracy'
)
model %>% fit(data, labels, epochs=5)
```

The learning rate schedule is also serializable and deserializable using
`keras$optimizers$schedules$serialize`

and
`keras$optimizers$schedules$deserialize`

.

## See also

Other optimizer learning rate schedules: `LearningRateSchedule()`

`learning_rate_schedule_cosine_decay()`

`learning_rate_schedule_cosine_decay_restarts()`

`learning_rate_schedule_exponential_decay()`

`learning_rate_schedule_inverse_time_decay()`

`learning_rate_schedule_piecewise_constant_decay()`