Defined in tensorflow/python/training/

See the guide: Training > Decaying the learning rate

Applies linear cosine decay to the learning rate.

See [Bello et al., ICML2017] Neural Optimizer Search with RL.

For the idea of warm starts here controlled by num_periods, see [Loshchilov & Hutter, ICLR2016] SGDR: Stochastic Gradient Descent with Warm Restarts.

Note that linear cosine decay is more aggressive than cosine decay and larger initial learning rates can typically be used.

When training a model, it is often recommended to lower the learning rate as the training progresses. This function applies a linear cosine decay function to a provided initial learning rate. It requires a global_step value to compute the decayed learning rate. You can just pass a TensorFlow variable that you increment at each training step.

The function returns the decayed learning rate. It is computed as:

global_step = min(global_step, decay_steps)
linear_decay = (decay_steps - global_step) / decay_steps)
cosine_decay = 0.5 * (
    1 + cos(pi * 2 * num_periods * global_step / decay_steps))
decayed = (alpha + linear_decay) * cosine_decay + beta
decayed_learning_rate = learning_rate * decayed

Example usage:

decay_steps = 1000
lr_decayed = linear_cosine_decay(learning_rate, global_step, decay_steps)


  • learning_rate: A scalar float32 or float64 Tensor or a Python number. The initial learning rate.
  • global_step: A scalar int32 or int64 Tensor or a Python number. Global step to use for the decay computation.
  • decay_steps: A scalar int32 or int64 Tensor or a Python number. Number of steps to decay over.
  • num_periods: Number of periods in the cosine part of the decay. See computation above.
  • alpha: See computation above.
  • beta: See computation above.
  • name: String. Optional name of the operation. Defaults to 'LinearCosineDecay'.


A scalar Tensor of the same type as learning_rate. The decayed learning rate.


  • ValueError: if global_step is not supplied.