# tf.compat.v1.train.noisy_linear_cosine_decay

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| [![](https://www.tensorflow.org/images/GitHub-Mark-32px.png) View source on GitHub](https://github.com/tensorflow/tensorflow/blob/v2.13.1/tensorflow/python/keras/optimizer_v2/legacy_learning_rate_decay.py#L682-L774) |

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
    )

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)

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| ## 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'. |

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

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| ## Raises ||
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| `ValueError` | if `global_step` is not supplied. |

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| ## References ||
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| Neural Optimizer Search with Reinforcement Learning: [Bello et al., 2017](http://proceedings.mlr.press/v70/bello17a.html) ([pdf](http://proceedings.mlr.press/v70/bello17a/bello17a.pdf)) Stochastic Gradient Descent with Warm Restarts: [Loshchilov et al., 2017](https://openreview.net/forum?id=Skq89Scxx&noteId=Skq89Scxx) ([pdf](https://openreview.net/pdf?id=Skq89Scxx)) ||

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## eager compatibility

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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.

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