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See Loshchilov & Hutter, ICLR2016, SGDR: Stochastic Gradient Descent with Warm Restarts.

For the idea of a linear warmup of our learning rate, see Goyal et al..

When we begin training a model, we often want an initial increase in our learning rate followed by a decay. If warmup_target is an int, this schedule applies a linear increase per optimizer step to our learning rate from initial_learning_rate to warmup_target for a duration of warmup_steps. Afterwards, it applies a cosine decay function taking our learning rate from warmup_target to alpha for a duration of decay_steps. If warmup_target is NULL we skip warmup and our decay will take our learning rate from initial_learning_rate to alpha. It requires a step value to compute the 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 warmup followed by 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.

Our warmup is computed as:

warmup_learning_rate <- function(step) {
  completed_fraction <- step / warmup_steps
  total_delta <- target_warmup - initial_learning_rate
  completed_fraction * total_delta

And our decay is computed as:

if (is.null(warmup_target)) {
  initial_decay_lr <- initial_learning_rate
} else {
  initial_decay_lr <- warmup_target

decayed_learning_rate <- function(step) {
  step <- min(step, decay_steps)
  cosine_decay <- 0.5 * (1 + cos(pi * step / decay_steps))
  decayed <- (1 - alpha) * cosine_decay + alpha
  initial_decay_lr * decayed

Example usage without warmup:

decay_steps <- 1000
initial_learning_rate <- 0.1
lr_decayed_fn <- learning_rate_schedule_cosine_decay(
    initial_learning_rate, decay_steps)

Example usage with warmup:

decay_steps <- 1000
initial_learning_rate <- 0
warmup_steps <- 1000
target_learning_rate <- 0.1
lr_warmup_decayed_fn <- learning_rate_schedule_cosine_decay(
    initial_learning_rate, decay_steps, warmup_target = target_learning_rate,
    warmup_steps = warmup_steps

You can pass this schedule directly into a optimizer as the learning rate. The learning rate schedule is also serializable and deserializable using keras$optimizers$schedules$serialize and keras$optimizers$schedules$deserialize.


  alpha = 0,
  name = "CosineDecay",
  warmup_target = NULL,
  warmup_steps = 0L



A float. The initial learning rate.


A int. Number of steps to decay over.


A float. Minimum learning rate value for decay as a fraction of initial_learning_rate.


String. Optional name of the operation. Defaults to "CosineDecay".


A float. The target learning rate for our warmup phase. Will cast to the initial_learning_rate datatype. Setting to NULL will skip warmup and begins decay phase from initial_learning_rate. Otherwise scheduler will warmup from initial_learning_rate to warmup_target.


A int. Number of steps to warmup over.


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.