class_docstr: A `LearningRateSchedule` that uses a polynomial decay schedule.
  
  It is commonly observed that a monotonically decreasing learning rate, whose
  degree of change is carefully chosen, results in a better performing model.
  This schedule applies a polynomial decay function to an optimizer step,
  given a provided `initial_learning_rate`, to reach an `end_learning_rate`
  in the given `decay_steps`.
  
  It requires a `step` value to compute the decayed learning rate. You
  can just pass a backend variable that you increment at each training
  step.
  
  The schedule is a 1-arg callable that produces a decayed learning rate
  when passed the current optimizer step. This can be useful for changing the
  learning rate value across different invocations of optimizer functions.
  It is computed as:
  
  ```python
  def decayed_learning_rate(step):
      step = min(step, decay_steps)
      return ((initial_learning_rate - end_learning_rate) *
              (1 - 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 `step`.
  
  ```python
  def decayed_learning_rate(step):
      decay_steps = decay_steps * ceil(step / decay_steps)
      return ((initial_learning_rate - end_learning_rate) *
              (1 - step / decay_steps) ^ (power)
             ) + end_learning_rate
  ```
  
  You can pass this schedule directly into a `keras.optimizers.Optimizer`
  as the learning rate.
  Example: Fit a model while decaying from 0.1 to 0.01 in 10000 steps using
  sqrt (i.e. power=0.5):
  
  ```python
  ...
  starter_learning_rate = 0.1
  end_learning_rate = 0.01
  decay_steps = 10000
  learning_rate_fn = keras.optimizers.schedules.PolynomialDecay(
      starter_learning_rate,
      decay_steps,
      end_learning_rate,
      power=0.5)
  
  model.compile(optimizer=keras.optimizers.SGD(
                    learning_rate=learning_rate_fn),
                loss='sparse_categorical_crossentropy',
                metrics=['accuracy'])
  
  model.fit(data, labels, epochs=5)
  ```
  
  The learning rate schedule is also serializable and deserializable using
  `keras.optimizers.schedules.serialize` and
  `keras.optimizers.schedules.deserialize`.
  
  Args:
      initial_learning_rate: A Python float. The initial learning rate.
      decay_steps: A Python integer. Must be positive. See the decay
          computation above.
      end_learning_rate: A Python float. The minimal end learning rate.
      power: A Python float. The power of the polynomial. Defaults to
          `1.0`.
      cycle: A boolean, whether it should cycle beyond decay_steps.
      name: String.  Optional name of the operation. Defaults to
          `"PolynomialDecay"`.
  
  Returns:
      A 1-arg callable learning rate schedule that takes the current optimizer
      step and outputs the decayed learning rate, a scalar tensor of the
      same type as `initial_learning_rate`.
code: def __call__(self, step):
      with ops.name_scope(self.name):
          initial_learning_rate = ops.convert_to_tensor(
              self.initial_learning_rate
          )
          dtype = initial_learning_rate.dtype
          end_learning_rate = ops.cast(self.end_learning_rate, dtype)
          power = ops.cast(self.power, dtype)
  
          global_step_recomp = ops.cast(step, dtype)
          decay_steps_recomp = ops.cast(self.decay_steps, dtype)
          if self.cycle:
              # Find the first multiple of decay_steps that is bigger than
              # global_step. If global_step is zero set the multiplier to 1
              multiplier = ops.where(
                  ops.equal(global_step_recomp, 0),
                  1.0,
                  ops.ceil(global_step_recomp / self.decay_steps),
              )
              decay_steps_recomp = ops.multiply(
                  decay_steps_recomp, multiplier
              )
          else:
              # Make sure that the global_step used is not bigger than
              # decay_steps.
              global_step_recomp = ops.minimum(
                  global_step_recomp, decay_steps_recomp
              )
  
          p = ops.divide(global_step_recomp, decay_steps_recomp)
          return ops.add(
              ops.multiply(
                  initial_learning_rate - end_learning_rate,
                  ops.power(1 - p, power),
              ),
              end_learning_rate,
          )
  
imports: import math
  from keras import ops
  from keras.api_export import keras_export
  from keras.saving import serialization_lib
label_desc: Use image node_id 2 for calling the PolynomialDecay obj's underlying member method code with example usage: obj.__call__(step) and returns: ops