# tf.compat.v1.train.cosine_decay_restarts

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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#L520-L594) |

Applies cosine decay with restarts to the learning rate.

    tf.compat.v1.train.cosine_decay_restarts(
        learning_rate,
        global_step,
        first_decay_steps,
        t_mul=2.0,
        m_mul=1.0,
        alpha=0.0,
        name=None
    )

When training a model, it is often recommended to lower the learning rate as
the training progresses. This function applies a cosine decay function with
restarts 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 while taking into account
possible warm restarts. 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 smaller initial learning rate.

#### Example usage:

    first_decay_steps = 1000
    lr_decayed = cosine_decay_restarts(learning_rate, global_step,
                                       first_decay_steps)

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| ## Args ||
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| `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. |
| `first_decay_steps` | A scalar `int32` or `int64` `Tensor` or a Python number. Number of steps to decay over. |
| `t_mul` | A scalar `float32` or `float64` `Tensor` or a Python number. Used to derive the number of iterations in the i-th period |
| `m_mul` | A scalar `float32` or `float64` `Tensor` or a Python number. Used to derive the initial learning rate of the i-th period: |
| `alpha` | A scalar `float32` or `float64` Tensor or a Python number. Minimum learning rate value as a fraction of the learning_rate. |
| `name` | String. Optional name of the operation. Defaults to 'SGDRDecay'. |

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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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| 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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