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

When training a model, it is often useful to lower the learning rate as the training progresses. This schedule applies a cosine decay function with restarts to an optimizer step, given a provided initial learning rate. 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.

The learning rate multiplier first decays from 1 to alpha for first_decay_steps steps. Then, a warm restart is performed. Each new warm restart runs for t_mul times more steps and with m_mul times initial learning rate as the new learning rate.

Example usage:

first_decay_steps <- 1000
lr_decayed_fn <- learning_rate_schedule_cosine_decay_restarts(

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.


  t_mul = 2,
  m_mul = 1,
  alpha = 0,
  name = "SGDRDecay"



A float. The initial learning rate.


An integer. Number of steps to decay over.


A float. Used to derive the number of iterations in the i-th period.


A float. Used to derive the initial learning rate of the i-th period.


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


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


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.