# learning_rate_schedule_polynomial_decay

## A LearningRateSchedule that uses a polynomial decay schedule

## Description

A LearningRateSchedule that uses a polynomial decay schedule

## Usage

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

## Arguments

Arguments | Description |
---|---|

initial_learning_rate | A scalar `float32` or `float64` `Tensor` or an R number. The initial learning rate. |

decay_steps | A scalar `int32` or `int64` `Tensor` or an R number. Must be positive. See the decay computation above. |

end_learning_rate | A scalar `float32` or `float64` `Tensor` or an R number. The minimal end learning rate. |

power | A scalar `float32` or `float64` `Tensor` or an R number. The power of the polynomial. Defaults to linear, 1.0. |

cycle | A boolean, whether or not it should cycle beyond decay_steps. |

… | For backwards and forwards compatibility |

name | String. Optional name of the operation. Defaults to ‘PolynomialDecay’. |

## Details

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 TensorFlow 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 * ceiling(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 keras Optimizer as the `learning_rate`. Example: 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)

```