# tf.compat.v1.train.polynomial_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#L185-L283) |

Applies a polynomial decay to the learning rate.

    tf.compat.v1.train.polynomial_decay(
        learning_rate,
        global_step,
        decay_steps,
        end_learning_rate=0.0001,
        power=1.0,
        cycle=False,
        name=None
    )

It is commonly observed that a monotonically decreasing learning rate, whose
degree of change is carefully chosen, results in a better performing model.
This function applies a polynomial decay function to a provided initial
`learning_rate` to reach an `end_learning_rate` in the given `decay_steps`.

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)
    decayed_learning_rate = (learning_rate - end_learning_rate) *
                            (1 - global_step / decay_steps) ^ (power) +
                            end_learning_rate

If `cycle` is True then a multiple of `decay_steps` is used, the first one
that is bigger than `global_steps`.

    decay_steps = decay_steps * ceil(global_step / decay_steps)
    decayed_learning_rate = (learning_rate - end_learning_rate) *
                            (1 - global_step / decay_steps) ^ (power) +
                            end_learning_rate

Example: decay from 0.1 to 0.01 in 10000 steps using sqrt (i.e. power=0.5):

    ...
    global_step = tf.Variable(0, trainable=False)
    starter_learning_rate = 0.1
    end_learning_rate = 0.01
    decay_steps = 10000
    learning_rate = tf.compat.v1.train.polynomial_decay(starter_learning_rate,
    global_step,
                                              decay_steps, end_learning_rate,
                                              power=0.5)
    # Passing global_step to minimize() will increment it at each step.
    learning_step = (
        tf.compat.v1.train.GradientDescentOptimizer(learning_rate)
        .minimize(...my loss..., global_step=global_step)
    )

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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. Must not be negative. |
| `decay_steps` | A scalar `int32` or `int64` `Tensor` or a Python number. Must be positive. See the decay computation above. |
| `end_learning_rate` | A scalar `float32` or `float64` `Tensor` or a Python number. The minimal end learning rate. |
| `power` | A scalar `float32` or `float64` `Tensor` or a Python number. The power of the polynomial. Defaults to linear, 1.0. |
| `cycle` | A boolean, whether or not it should cycle beyond decay_steps. |
| `name` | String. Optional name of the operation. Defaults to 'PolynomialDecay'. |

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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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## 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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