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Applies noisy 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 noisy 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 + eps_t) * cosine_decay + beta
decayed_learning_rate = learning_rate * decayed

where eps_t is 0-centered gaussian noise with variance initial_variance / (1 + global_step) ** variance_decay

Example usage:

decay_steps = 1000
lr_decayed = noisy_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.
initial_variance initial variance for the noise. See computation above.
variance_decay decay for the noise's variance. See computation above.
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 'NoisyLinearCosineDecay'.

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

ValueError if global_step is not supplied.

Eager Compatibility

When eager execution is enabled, this function returns a function which in turn returns the decayed learning rate Tensor. This can be useful for changing the learning rate value across different invocations of optimizer functions.