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# tf.compat.v1.train.polynomial_decay

Applies a polynomial decay to the learning rate.

### Used in the notebooks

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 = (
.minimize(...my loss..., global_step=global_step)
)
``````

`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'.

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.

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