text: # Copyright 2015 The TensorFlow Authors. All Rights Reserved.
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  #     http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  # ==============================================================================
  """Various learning rate decay functions."""
  
  import tensorflow.compat.v2 as tf
  
  import abc
  import math
  from keras.utils import generic_utils
  from tensorflow.python.util.tf_export import keras_export
  
  
  @keras_export("keras.optimizers.schedules.LearningRateSchedule")
  class LearningRateSchedule(object):
    """The learning rate schedule base class.
  
    You can use a learning rate schedule to modulate how the learning rate
    of your optimizer changes over time.
  
    Several built-in learning rate schedules are available, such as
    `tf.keras.optimizers.schedules.ExponentialDecay` or
    `tf.keras.optimizers.schedules.PiecewiseConstantDecay`:
  
    ```python
    lr_schedule = keras.optimizers.schedules.ExponentialDecay(
        initial_learning_rate=1e-2,
        decay_steps=10000,
        decay_rate=0.9)
    optimizer = keras.optimizers.SGD(learning_rate=lr_schedule)
    ```
  
    A `LearningRateSchedule` instance can be passed in as the `learning_rate`
    argument of any optimizer.
  
    To implement your own schedule object, you should implement the `__call__`
    method, which takes a `step` argument (scalar integer tensor, the
    current training step count).
    Like for any other Keras object, you can also optionally
    make your object serializable by implementing the `get_config`
    and `from_config` methods.
  
    Example:
  
    ```python
    class MyLRSchedule(tf.keras.optimizers.schedules.LearningRateSchedule):
  
      def __init__(self, initial_learning_rate):
        self.initial_learning_rate = initial_learning_rate
  
      def __call__(self, step):
         return self.initial_learning_rate / (step + 1)
  
    optimizer = tf.keras.optimizers.SGD(learning_rate=MyLRSchedule(0.1))
    ```
    """
  
    @abc.abstractmethod
    def __call__(self, step):
      raise NotImplementedError("Learning rate schedule must override __call__")
  
    @abc.abstractmethod
    def get_config(self):
      raise NotImplementedError("Learning rate schedule must override get_config")
  
    @classmethod
    def from_config(cls, config):
      """Instantiates a `LearningRateSchedule` from its config.
  
      Args:
          config: Output of `get_config()`.
  
      Returns:
          A `LearningRateSchedule` instance.
      """
      return cls(**config)
  
  
  @keras_export("keras.optimizers.schedules.ExponentialDecay")
  class ExponentialDecay(LearningRateSchedule):
    """A LearningRateSchedule that uses an exponential decay schedule.
  
    When training a model, it is often useful to lower the learning rate as
    the training progresses. This schedule applies an exponential decay function
    to an optimizer step, given a provided initial learning rate.
  
    The schedule 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):
      return initial_learning_rate * decay_rate ^ (step / decay_steps)
    ```
  
    If the argument `staircase` is `True`, then `step / decay_steps` is
    an integer division and the decayed learning rate follows a
    staircase function.
  
    You can pass this schedule directly into a `tf.keras.optimizers.Optimizer`
    as the learning rate.
    Example: When fitting a Keras model, decay every 100000 steps with a base
    of 0.96:
  
    ```python
    initial_learning_rate = 0.1
    lr_schedule = tf.keras.optimizers.schedules.ExponentialDecay(
        initial_learning_rate,
        decay_steps=100000,
        decay_rate=0.96,
        staircase=True)
  
    model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=lr_schedule),
                  loss='sparse_categorical_crossentropy',
                  metrics=['accuracy'])
  
    model.fit(data, labels, epochs=5)
    ```
  
    The learning rate schedule is also serializable and deserializable using
    `tf.keras.optimizers.schedules.serialize` and
    `tf.keras.optimizers.schedules.deserialize`.
  
    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`.
    """
  
    def __init__(
        self,
        initial_learning_rate,
        decay_steps,
        decay_rate,
        staircase=False,
        name=None):
      """Applies exponential decay to the learning rate.
  
      Args:
        initial_learning_rate: A scalar `float32` or `float64` `Tensor` or a
          Python number.  The initial learning rate.
        decay_steps: A scalar `int32` or `int64` `Tensor` or a Python number.
          Must be positive.  See the decay computation above.
        decay_rate: A scalar `float32` or `float64` `Tensor` or a
          Python number.  The decay rate.
        staircase: Boolean.  If `True` decay the learning rate at discrete
          intervals
        name: String.  Optional name of the operation.  Defaults to
          'ExponentialDecay'.
      """
      super(ExponentialDecay, self).__init__()
      self.initial_learning_rate = initial_learning_rate
      self.decay_steps = decay_steps
      self.decay_rate = decay_rate
      self.staircase = staircase
      self.name = name
  
    def __call__(self, step):
      with tf.name_scope(self.name or "ExponentialDecay") as name:
        initial_learning_rate = tf.convert_to_tensor(
            self.initial_learning_rate, name="initial_learning_rate")
        dtype = initial_learning_rate.dtype
        decay_steps = tf.cast(self.decay_steps, dtype)
        decay_rate = tf.cast(self.decay_rate, dtype)
  
        global_step_recomp = tf.cast(step, dtype)
        p = global_step_recomp / decay_steps
        if self.staircase:
          p = tf.floor(p)
        return tf.multiply(
            initial_learning_rate, tf.pow(decay_rate, p), name=name)
  
    def get_config(self):
      return {
          "initial_learning_rate": self.initial_learning_rate,
          "decay_steps": self.decay_steps,
          "decay_rate": self.decay_rate,
          "staircase": self.staircase,
          "name": self.name
      }
  
  
  @keras_export("keras.optimizers.schedules.PiecewiseConstantDecay")
  class PiecewiseConstantDecay(LearningRateSchedule):
    """A LearningRateSchedule that uses a piecewise constant decay schedule.
  
    The function returns a 1-arg callable to compute the piecewise constant
    when passed the current optimizer step. This can be useful for changing the
    learning rate value across different invocations of optimizer functions.
  
    Example: use a learning rate that's 1.0 for the first 100001 steps, 0.5
      for the next 10000 steps, and 0.1 for any additional steps.
  
    ```python
    step = tf.Variable(0, trainable=False)
    boundaries = [100000, 110000]
    values = [1.0, 0.5, 0.1]
    learning_rate_fn = keras.optimizers.schedules.PiecewiseConstantDecay(
        boundaries, values)
  
    # Later, whenever we perform an optimization step, we pass in the step.
    learning_rate = learning_rate_fn(step)
    ```
  
    You can pass this schedule directly into a `tf.keras.optimizers.Optimizer`
    as the learning rate. The learning rate schedule is also serializable and
    deserializable using `tf.keras.optimizers.schedules.serialize` and
    `tf.keras.optimizers.schedules.deserialize`.
  
    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 the boundary tensors.
  
      The output of the 1-arg function that takes the `step`
      is `values[0]` when `step <= boundaries[0]`,
      `values[1]` when `step > boundaries[0]` and `step <= boundaries[1]`, ...,
      and values[-1] when `step > boundaries[-1]`.
    """
  
    def __init__(
        self,
        boundaries,
        values,
        name=None):
      """Piecewise constant from boundaries and interval values.
  
      Args:
        boundaries: A list of `Tensor`s or `int`s or `float`s with strictly
          increasing entries, and with all elements having the same type as the
          optimizer step.
        values: A list of `Tensor`s or `float`s or `int`s that specifies the
          values for the intervals defined by `boundaries`. It should have one
          more element than `boundaries`, and all elements should have the same
          type.
        name: A string. Optional name of the operation. Defaults to
          'PiecewiseConstant'.
  
      Raises:
        ValueError: if the number of elements in the lists do not match.
      """
      super(PiecewiseConstantDecay, self).__init__()
  
      if len(boundaries) != len(values) - 1:
        raise ValueError(
            "The length of boundaries should be 1 less than the length of values")
  
      self.boundaries = boundaries
      self.values = values
      self.name = name
  
    def __call__(self, step):
      with tf.name_scope(self.name or "PiecewiseConstant"):
        boundaries = tf.nest.map_structure(tf.convert_to_tensor,
                                        tf.nest.flatten(self.boundaries))
        values = tf.nest.map_structure(tf.convert_to_tensor,
                                    tf.nest.flatten(self.values))
        x_recomp = tf.convert_to_tensor(step)
        for i, b in enumerate(boundaries):
          if b.dtype.base_dtype != x_recomp.dtype.base_dtype:
            # We cast the boundaries to have the same type as the step
            b = tf.cast(b, x_recomp.dtype.base_dtype)
            boundaries[i] = b
        pred_fn_pairs = []
        pred_fn_pairs.append((x_recomp <= boundaries[0], lambda: values[0]))
        pred_fn_pairs.append((x_recomp > boundaries[-1], lambda: values[-1]))
        for low, high, v in zip(boundaries[:-1], boundaries[1:], values[1:-1]):
          # Need to bind v here; can do this with lambda v=v: ...
          pred = (x_recomp > low) & (x_recomp <= high)
          pred_fn_pairs.append((pred, lambda v=v: v))
  
        # The default isn't needed here because our conditions are mutually
        # exclusive and exhaustive, but tf.case requires it.
        default = lambda: values[0]
        return tf.compat.v1.case(pred_fn_pairs, default, exclusive=True)
  
    def get_config(self):
      return {
          "boundaries": self.boundaries,
          "values": self.values,
          "name": self.name
      }
  
  
  @keras_export("keras.optimizers.schedules.PolynomialDecay")
  class PolynomialDecay(LearningRateSchedule):
    """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 TensorFlow 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 `tf.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 = tf.keras.optimizers.schedules.PolynomialDecay(
        starter_learning_rate,
        decay_steps,
        end_learning_rate,
        power=0.5)
  
    model.compile(optimizer=tf.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
    `tf.keras.optimizers.schedules.serialize` and
    `tf.keras.optimizers.schedules.deserialize`.
  
    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`.
    """
  
    def __init__(
        self,
        initial_learning_rate,
        decay_steps,
        end_learning_rate=0.0001,
        power=1.0,
        cycle=False,
        name=None):
      """Applies a polynomial decay to the learning rate.
  
      Args:
        initial_learning_rate: A scalar `float32` or `float64` `Tensor` or a
          Python number.  The initial learning rate.
        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'.
      """
      super(PolynomialDecay, self).__init__()
  
      self.initial_learning_rate = initial_learning_rate
      self.decay_steps = decay_steps
      self.end_learning_rate = end_learning_rate
      self.power = power
      self.cycle = cycle
      self.name = name
  
    def __call__(self, step):
      with tf.name_scope(self.name or "PolynomialDecay") as name:
        initial_learning_rate = tf.convert_to_tensor(
            self.initial_learning_rate, name="initial_learning_rate")
        dtype = initial_learning_rate.dtype
        end_learning_rate = tf.cast(self.end_learning_rate, dtype)
        power = tf.cast(self.power, dtype)
  
        global_step_recomp = tf.cast(step, dtype)
        decay_steps_recomp = tf.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 = tf.compat.v1.cond(
              tf.equal(global_step_recomp, 0), lambda: 1.0,
              lambda: tf.math.ceil(global_step_recomp / self.decay_steps))
          decay_steps_recomp = tf.multiply(decay_steps_recomp, multiplier)
        else:
          # Make sure that the global_step used is not bigger than decay_steps.
          global_step_recomp = tf.minimum(global_step_recomp,
                                                decay_steps_recomp)
  
        p = tf.divide(global_step_recomp, decay_steps_recomp)
        return tf.add(
            tf.multiply(initial_learning_rate - end_learning_rate,
                              tf.pow(1 - p, power)),
            end_learning_rate,
            name=name)
  
    def get_config(self):
      return {
          "initial_learning_rate": self.initial_learning_rate,
          "decay_steps": self.decay_steps,
          "end_learning_rate": self.end_learning_rate,
          "power": self.power,
          "cycle": self.cycle,
          "name": self.name
      }
  
  
  @keras_export("keras.optimizers.schedules.InverseTimeDecay")
  class InverseTimeDecay(LearningRateSchedule):
    """A LearningRateSchedule that uses an inverse time decay schedule.
  
    When training a model, it is often useful to lower the learning rate as
    the training progresses. This schedule applies the inverse decay function
    to an optimizer step, given a provided initial learning rate.
    It requires a `step` value to compute the decayed learning rate. You can
    just pass a TensorFlow variable that you increment at each training step.
  
    The schedule 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):
      return initial_learning_rate / (1 + decay_rate * step / decay_step)
    ```
  
    or, if `staircase` is `True`, as:
  
    ```python
    def decayed_learning_rate(step):
      return initial_learning_rate / (1 + decay_rate * floor(step / decay_step))
    ```
  
    You can pass this schedule directly into a `tf.keras.optimizers.Optimizer`
    as the learning rate.
    Example: Fit a Keras model when decaying 1/t with a rate of 0.5:
  
    ```python
    ...
    initial_learning_rate = 0.1
    decay_steps = 1.0
    decay_rate = 0.5
    learning_rate_fn = keras.optimizers.schedules.InverseTimeDecay(
      initial_learning_rate, decay_steps, decay_rate)
  
    model.compile(optimizer=tf.keras.optimizers.SGD(
                      learning_rate=learning_rate_fn),
                  loss='sparse_categorical_crossentropy',
                  metrics=['accuracy'])
  
    model.fit(data, labels, epochs=5)
    ```
  
    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`.
    """
  
    def __init__(
        self,
        initial_learning_rate,
        decay_steps,
        decay_rate,
        staircase=False,
        name=None):
      """Applies inverse time decay to the initial learning rate.
  
      Args:
        initial_learning_rate: A scalar `float32` or `float64` `Tensor` or a
          Python number.  The initial learning rate.
        decay_steps: How often to apply decay.
        decay_rate: A Python number.  The decay rate.
        staircase: Whether to apply decay in a discrete staircase, as opposed to
          continuous, fashion.
        name: String.  Optional name of the operation.  Defaults to
          'InverseTimeDecay'.
      """
      super(InverseTimeDecay, self).__init__()
  
      self.initial_learning_rate = initial_learning_rate
      self.decay_steps = decay_steps
      self.decay_rate = decay_rate
      self.staircase = staircase
      self.name = name
  
    def __call__(self, step):
      with tf.name_scope(self.name or "InverseTimeDecay") as name:
        initial_learning_rate = tf.convert_to_tensor(
            self.initial_learning_rate, name="initial_learning_rate")
        dtype = initial_learning_rate.dtype
        decay_steps = tf.cast(self.decay_steps, dtype)
        decay_rate = tf.cast(self.decay_rate, dtype)
  
        global_step_recomp = tf.cast(step, dtype)
        p = global_step_recomp / decay_steps
        if self.staircase:
          p = tf.floor(p)
        const = tf.cast(tf.constant(1), dtype)
        denom = tf.add(const, tf.multiply(decay_rate, p))
        return tf.divide(initial_learning_rate, denom, name=name)
  
    def get_config(self):
      return {
          "initial_learning_rate": self.initial_learning_rate,
          "decay_steps": self.decay_steps,
          "decay_rate": self.decay_rate,
          "staircase": self.staircase,
          "name": self.name
      }
  
  
  @keras_export("keras.optimizers.schedules.CosineDecay",
                "keras.experimental.CosineDecay")
  class CosineDecay(LearningRateSchedule):
    """A LearningRateSchedule that uses a cosine decay schedule.
  
    See [Loshchilov & Hutter, ICLR2016](https://arxiv.org/abs/1608.03983),
    SGDR: Stochastic Gradient Descent with Warm Restarts.
  
    When training a model, it is often useful to lower the learning rate as
    the training progresses. This schedule applies a cosine decay function
    to an optimizer step, given a provided initial learning rate.
    It requires a `step` value to compute the decayed learning rate. You can
    just pass a TensorFlow variable that you increment at each training step.
  
    The schedule 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)
      cosine_decay = 0.5 * (1 + cos(pi * step / decay_steps))
      decayed = (1 - alpha) * cosine_decay + alpha
      return initial_learning_rate * decayed
    ```
  
    Example usage:
    ```python
    decay_steps = 1000
    lr_decayed_fn = tf.keras.optimizers.schedules.CosineDecay(
        initial_learning_rate, decay_steps)
    ```
  
    You can pass this schedule directly into a `tf.keras.optimizers.Optimizer`
    as the learning rate. The learning rate schedule is also serializable and
    deserializable using `tf.keras.optimizers.schedules.serialize` and
    `tf.keras.optimizers.schedules.deserialize`.
  
    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`.
    """
  
    def __init__(
        self,
        initial_learning_rate,
        decay_steps,
        alpha=0.0,
        name=None):
      """Applies cosine decay to the learning rate.
  
      Args:
        initial_learning_rate: A scalar `float32` or `float64` Tensor or a
          Python number. The initial learning rate.
        decay_steps: A scalar `int32` or `int64` `Tensor` or a Python number.
          Number of steps to decay over.
        alpha: A scalar `float32` or `float64` Tensor or a Python number.
          Minimum learning rate value as a fraction of initial_learning_rate.
        name: String. Optional name of the operation.  Defaults to 'CosineDecay'.
      """
      super(CosineDecay, self).__init__()
  
      self.initial_learning_rate = initial_learning_rate
      self.decay_steps = decay_steps
      self.alpha = alpha
      self.name = name
  
    def __call__(self, step):
      with tf.name_scope(self.name or "CosineDecay"):
        initial_learning_rate = tf.convert_to_tensor(
            self.initial_learning_rate, name="initial_learning_rate")
        dtype = initial_learning_rate.dtype
        decay_steps = tf.cast(self.decay_steps, dtype)
  
        global_step_recomp = tf.cast(step, dtype)
        global_step_recomp = tf.minimum(global_step_recomp, decay_steps)
        completed_fraction = global_step_recomp / decay_steps
        cosine_decayed = 0.5 * (1.0 + tf.cos(
            tf.constant(math.pi) * completed_fraction))
  
        decayed = (1 - self.alpha) * cosine_decayed + self.alpha
        return tf.multiply(initial_learning_rate, decayed)
  
    def get_config(self):
      return {
          "initial_learning_rate": self.initial_learning_rate,
          "decay_steps": self.decay_steps,
          "alpha": self.alpha,
          "name": self.name
      }
  
  
  @keras_export("keras.optimizers.schedules.CosineDecayRestarts",
                "keras.experimental.CosineDecayRestarts")
  class CosineDecayRestarts(LearningRateSchedule):
    """A LearningRateSchedule that uses a cosine decay schedule with restarts.
  
    See [Loshchilov & Hutter, ICLR2016](https://arxiv.org/abs/1608.03983),
    SGDR: Stochastic Gradient Descent with Warm Restarts.
  
    When training a model, it is often useful to lower the learning rate as
    the training progresses. This schedule applies a cosine decay function with
    restarts to an optimizer step, given a provided initial learning rate.
    It requires a `step` value to compute the decayed learning rate. You can
    just pass a TensorFlow variable that you increment at each training step.
  
    The schedule 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.
  
    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:
    ```python
    first_decay_steps = 1000
    lr_decayed_fn = (
      tf.keras.optimizers.schedules.CosineDecayRestarts(
          initial_learning_rate,
          first_decay_steps))
    ```
  
    You can pass this schedule directly into a `tf.keras.optimizers.Optimizer`
    as the learning rate. The learning rate schedule is also serializable and
    deserializable using `tf.keras.optimizers.schedules.serialize` and
    `tf.keras.optimizers.schedules.deserialize`.
  
    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`.
    """
  
    def __init__(
        self,
        initial_learning_rate,
        first_decay_steps,
        t_mul=2.0,
        m_mul=1.0,
        alpha=0.0,
        name=None):
      """Applies cosine decay with restarts to the learning rate.
  
      Args:
        initial_learning_rate: A scalar `float32` or `float64` Tensor or a Python
          number. The initial learning rate.
        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 initial_learning_rate.
        name: String. Optional name of the operation.  Defaults to 'SGDRDecay'.
      """
      super(CosineDecayRestarts, self).__init__()
  
      self.initial_learning_rate = initial_learning_rate
      self.first_decay_steps = first_decay_steps
      self._t_mul = t_mul
      self._m_mul = m_mul
      self.alpha = alpha
      self.name = name
  
    def __call__(self, step):
      with tf.name_scope(self.name or "SGDRDecay") as name:
        initial_learning_rate = tf.convert_to_tensor(
            self.initial_learning_rate, name="initial_learning_rate")
        dtype = initial_learning_rate.dtype
        first_decay_steps = tf.cast(self.first_decay_steps, dtype)
        alpha = tf.cast(self.alpha, dtype)
        t_mul = tf.cast(self._t_mul, dtype)
        m_mul = tf.cast(self._m_mul, dtype)
  
        global_step_recomp = tf.cast(step, dtype)
        completed_fraction = global_step_recomp / first_decay_steps
  
        def compute_step(completed_fraction, geometric=False):
          """Helper for `cond` operation."""
          if geometric:
            i_restart = tf.floor(
                tf.math.log(1.0 - completed_fraction * (1.0 - t_mul)) /
                tf.math.log(t_mul))
  
            sum_r = (1.0 - t_mul**i_restart) / (1.0 - t_mul)
            completed_fraction = (completed_fraction - sum_r) / t_mul**i_restart
  
          else:
            i_restart = tf.floor(completed_fraction)
            completed_fraction -= i_restart
  
          return i_restart, completed_fraction
  
        i_restart, completed_fraction = tf.compat.v1.cond(
            tf.equal(t_mul, 1.0),
            lambda: compute_step(completed_fraction, geometric=False),
            lambda: compute_step(completed_fraction, geometric=True))
  
        m_fac = m_mul**i_restart
        cosine_decayed = 0.5 * m_fac * (1.0 + tf.cos(
            tf.constant(math.pi) * completed_fraction))
        decayed = (1 - alpha) * cosine_decayed + alpha
  
        return tf.multiply(initial_learning_rate, decayed, name=name)
  
    def get_config(self):
      return {
          "initial_learning_rate": self.initial_learning_rate,
          "first_decay_steps": self.first_decay_steps,
          "t_mul": self._t_mul,
          "m_mul": self._m_mul,
          "alpha": self.alpha,
          "name": self.name
      }
  
  
  # Note: this code is still used by V1 APIs.
  class LinearCosineDecay(LearningRateSchedule):
    """A LearningRateSchedule that uses a linear cosine decay schedule.
  
    See [Bello et al., ICML2017] Neural Optimizer Search with RL.
    https://arxiv.org/abs/1709.07417
  
    For the idea of warm starts here controlled by `num_periods`,
    see [Loshchilov & Hutter, ICLR2016] SGDR: Stochastic Gradient Descent
    with Warm Restarts. https://arxiv.org/abs/1608.03983
  
    Note that linear cosine decay is more aggressive than cosine decay and
    larger initial learning rates can typically be used.
  
    When training a model, it is often recommended to lower the learning rate as
    the training progresses. This schedule applies a linear cosine decay
    function to an optimizer step, given a provided initial learning rate.
    It requires a `step` value to compute the decayed learning rate. You can
    just pass a TensorFlow variable that you increment at each training step.
  
    The schedule 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)
      linear_decay = (decay_steps - step) / decay_steps
      cosine_decay = 0.5 * (
          1 + cos(pi * 2 * num_periods * step / decay_steps))
      decayed = (alpha + linear_decay) * cosine_decay + beta
      return initial_learning_rate * decayed
    ```
  
    Example usage:
    ```python
    decay_steps = 1000
    lr_decayed_fn = (
      tf.keras.experimental.LinearCosineDecay(
        initial_learning_rate, decay_steps))
    ```
  
    You can pass this schedule directly into a `tf.keras.optimizers.Optimizer`
    as the learning rate. The learning rate schedule is also serializable and
    deserializable using `tf.keras.optimizers.schedules.serialize` and
    `tf.keras.optimizers.schedules.deserialize`.
  
    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`.
    """
  
    def __init__(
        self,
        initial_learning_rate,
        decay_steps,
        num_periods=0.5,
        alpha=0.0,
        beta=0.001,
        name=None):
      """Applies linear cosine decay to the learning rate.
  
      Args:
        initial_learning_rate: A scalar `float32` or `float64` Tensor or a Python
          number. The initial learning rate.
        decay_steps: A scalar `int32` or `int64` `Tensor` or a Python number.
          Number of steps to decay over.
        num_periods: Number of periods in the cosine part of the decay.
          See computation above.
        alpha: See computation above.
        beta: See computation above.
        name: String.  Optional name of the operation.  Defaults to
          'LinearCosineDecay'.
      """
      super(LinearCosineDecay, self).__init__()
  
      self.initial_learning_rate = initial_learning_rate
      self.decay_steps = decay_steps
      self.num_periods = num_periods
      self.alpha = alpha
      self.beta = beta
      self.name = name
  
    def __call__(self, step):
      with tf.name_scope(self.name or "LinearCosineDecay") as name:
        initial_learning_rate = tf.convert_to_tensor(
            self.initial_learning_rate, name="initial_learning_rate")
        dtype = initial_learning_rate.dtype
        decay_steps = tf.cast(self.decay_steps, dtype)
        num_periods = tf.cast(self.num_periods, dtype)
        alpha = tf.cast(self.alpha, dtype)
        beta = tf.cast(self.beta, dtype)
  
        global_step_recomp = tf.cast(step, dtype)
        global_step_recomp = tf.minimum(global_step_recomp, decay_steps)
        linear_decayed = (decay_steps - global_step_recomp) / decay_steps
        completed_fraction = global_step_recomp / decay_steps
        fraction = 2.0 * num_periods * completed_fraction
        cosine_decayed = 0.5 * (
            1.0 + tf.cos(tf.constant(math.pi) * fraction))
  
        linear_cosine_decayed = (alpha + linear_decayed) * cosine_decayed + beta
        return tf.multiply(initial_learning_rate, linear_cosine_decayed,
                                 name=name)
  
    def get_config(self):
      return {
          "initial_learning_rate": self.initial_learning_rate,
          "decay_steps": self.decay_steps,
          "num_periods": self.num_periods,
          "alpha": self.alpha,
          "beta": self.beta,
          "name": self.name
      }
  
  
  # Note: this code is still used by V1 APIs.
  class NoisyLinearCosineDecay(LearningRateSchedule):
    """A LearningRateSchedule that uses a noisy linear cosine decay schedule.
  
    See [Bello et al., ICML2017] Neural Optimizer Search with RL.
    https://arxiv.org/abs/1709.07417
  
    For the idea of warm starts here controlled by `num_periods`,
    see [Loshchilov & Hutter, ICLR2016] SGDR: Stochastic Gradient Descent
    with Warm Restarts. https://arxiv.org/abs/1608.03983
  
    Note that linear cosine decay is more aggressive than cosine decay and
    larger initial learning rates can typically be used.
  
    When training a model, it is often recommended to lower the learning rate as
    the training progresses. This schedule applies a noisy linear cosine decay
    function to an optimizer step, given a provided initial learning rate.
    It requires a `step` value to compute the decayed learning rate. You can
    just pass a TensorFlow variable that you increment at each training step.
  
    The schedule 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)
      linear_decay = (decay_steps - step) / decay_steps)
      cosine_decay = 0.5 * (
          1 + cos(pi * 2 * num_periods * step / decay_steps))
      decayed = (alpha + linear_decay + eps_t) * cosine_decay + beta
      return initial_learning_rate * decayed
    ```
    where eps_t is 0-centered gaussian noise with variance
    initial_variance / (1 + global_step) ** variance_decay
  
    Example usage:
    ```python
    decay_steps = 1000
    lr_decayed_fn = (
      tf.keras.experimental.NoisyLinearCosineDecay(
        initial_learning_rate, decay_steps))
    ```
  
    You can pass this schedule directly into a `tf.keras.optimizers.Optimizer`
    as the learning rate. The learning rate schedule is also serializable and
    deserializable using `tf.keras.optimizers.schedules.serialize` and
    `tf.keras.optimizers.schedules.deserialize`.
  
    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`.
    """
  
    def __init__(
        self,
        initial_learning_rate,
        decay_steps,
        initial_variance=1.0,
        variance_decay=0.55,
        num_periods=0.5,
        alpha=0.0,
        beta=0.001,
        name=None):
      """Applies noisy linear cosine decay to the learning rate.
  
      Args:
        initial_learning_rate: A scalar `float32` or `float64` Tensor or a Python
          number. The initial learning rate.
        decay_steps: A scalar `int32` or `int64` `Tensor` or a Python number.
          Number of steps to decay over.
        initial_variance: initial variance for the noise. See computation above.
        variance_decay: decay for the noise's variance. See computation above.
        num_periods: Number of periods in the cosine part of the decay.
          See computation above.
        alpha: See computation above.
        beta: See computation above.
        name: String.  Optional name of the operation.  Defaults to
          'NoisyLinearCosineDecay'.
      """
      super(NoisyLinearCosineDecay, self).__init__()
  
      self.initial_learning_rate = initial_learning_rate
      self.decay_steps = decay_steps
      self.initial_variance = initial_variance
      self.variance_decay = variance_decay
      self.num_periods = num_periods
      self.alpha = alpha
      self.beta = beta
      self.name = name
  
    def __call__(self, step):
      with tf.name_scope(self.name or "NoisyLinearCosineDecay") as name:
        initial_learning_rate = tf.convert_to_tensor(
            self.initial_learning_rate, name="initial_learning_rate")
        dtype = initial_learning_rate.dtype
        decay_steps = tf.cast(self.decay_steps, dtype)
        initial_variance = tf.cast(self.initial_variance, dtype)
        variance_decay = tf.cast(self.variance_decay, dtype)
        num_periods = tf.cast(self.num_periods, dtype)
        alpha = tf.cast(self.alpha, dtype)
        beta = tf.cast(self.beta, dtype)
  
        global_step_recomp = tf.cast(step, dtype)
        global_step_recomp = tf.minimum(global_step_recomp, decay_steps)
        linear_decayed = (decay_steps - global_step_recomp) / decay_steps
        variance = initial_variance / (
            tf.pow(1.0 + global_step_recomp, variance_decay))
        std = tf.sqrt(variance)
        noisy_linear_decayed = (
            linear_decayed + tf.random.normal(
                linear_decayed.shape, stddev=std))
  
        completed_fraction = global_step_recomp / decay_steps
        fraction = 2.0 * num_periods * completed_fraction
        cosine_decayed = 0.5 * (
            1.0 + tf.cos(tf.constant(math.pi) * fraction))
        noisy_linear_cosine_decayed = (
            (alpha + noisy_linear_decayed) * cosine_decayed + beta)
  
        return tf.multiply(
            initial_learning_rate, noisy_linear_cosine_decayed, name=name)
  
    def get_config(self):
      return {
          "initial_learning_rate": self.initial_learning_rate,
          "decay_steps": self.decay_steps,
          "initial_variance": self.initial_variance,
          "variance_decay": self.variance_decay,
          "num_periods": self.num_periods,
          "alpha": self.alpha,
          "beta": self.beta,
          "name": self.name
      }
  
  
  @keras_export("keras.optimizers.schedules.serialize")
  def serialize(learning_rate_schedule):
    return generic_utils.serialize_keras_object(learning_rate_schedule)
  
  
  @keras_export("keras.optimizers.schedules.deserialize")
  def deserialize(config, custom_objects=None):
    return generic_utils.deserialize_keras_object(
        config,
        module_objects=globals(),
        custom_objects=custom_objects,
        printable_module_name="decay")
  