code: def polynomial_decay(
      learning_rate,
      global_step,
      decay_steps,
      end_learning_rate=0.0001,
      power=1.0,
      cycle=False,
      name=None,
  ):
      """Applies a polynomial decay to the learning rate.
  
      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:
  
      ```python
      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`.
  
      ```python
      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):
  
      ```python
      ...
      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)
      )
      ```
  
      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'.
  
      Returns:
        A scalar `Tensor` of the same type as `learning_rate`.  The decayed
        learning rate.
  
      Raises:
        ValueError: if `global_step` is not supplied.
  
      @compatibility(eager)
      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.
      @end_compatibility
      """
      decayed_lr = learning_rate_schedule.PolynomialDecay(
          learning_rate,
          decay_steps,
          end_learning_rate=end_learning_rate,
          power=power,
          cycle=cycle,
          name=name,
      )
  
      if not context.executing_eagerly():
          decayed_lr = decayed_lr(global_step)
      else:
          decayed_lr = functools.partial(decayed_lr, global_step)
      return decayed_lr
  
file_path: tensorflow-upstream/tensorflow/python/keras/optimizer_v2/legacy_learning_rate_decay.py
imports: import functools
  from tensorflow.python.eager import context
  from tensorflow.python.framework import dtypes
  from tensorflow.python.framework import tensor_conversion
  from tensorflow.python.keras.optimizer_v2 import learning_rate_schedule
  from tensorflow.python.ops import math_ops
  from tensorflow.python.util import nest
  from tensorflow.python.util.tf_export import tf_export
label_desc: Use image node_id 3 for calling a global function with example usage: polynomial_decay(learning_rate, global_step, decay_steps, end_learning_rate, power, cycle, name) and returns: decayed_lr