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# tf.compat.v1.train.noisy_linear_cosine_decay

Applies noisy linear cosine decay to the learning rate.

``````tf.compat.v1.train.noisy_linear_cosine_decay(
learning_rate, global_step, decay_steps, initial_variance=1.0,
variance_decay=0.55, num_periods=0.5, alpha=0.0, beta=0.001, name=None
)
``````

See [Bello et al., ICML2017] Neural Optimizer Search with RL. https://arxiv.org/abs/1709.07417

For the idea of warm starts here controlled by `num_periods`, see [Loshchilov & Hutter, ICLR2016] SGDR: Stochastic Gradient Descent with Warm Restarts. https://arxiv.org/abs/1608.03983

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)
``````

#### Args:

• `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'.

#### Returns:

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

#### Raises:

• `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.