# 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 schedule functions.""" import abc import math import tensorflow.compat.v2 as tf from keras import backend from keras.utils import generic_utils # isort: off from tensorflow.python.util.tf_export import keras_export @keras_export("keras.optimizers.schedules.LearningRateSchedule") class LearningRateSchedule: """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 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): 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().__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().__init__() if len(boundaries) != len(values) - 1: raise ValueError( "The length of boundaries should be 1 less than the length of " f"values. Received: boundaries={boundaries} of length " f"{len(boundaries)}, and values={values} " f"of length {len(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.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().__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.where( tf.equal(global_step_recomp, 0), 1.0, 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 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): 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().__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 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) 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().__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, dtype=dtype) * 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 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. 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 initial learning rate as the new 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().__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.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, dtype=dtype) * 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 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) 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().__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, dtype=dtype) * 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 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) 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, seed=None, 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. seed: Integer, optional random seed to enable deterministic behavior. name: String. Optional name of the operation. Defaults to 'NoisyLinearCosineDecay'. """ super().__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.seed = seed self.name = name self._random_generator = backend.RandomGenerator(seed) 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 + self._random_generator.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, dtype=dtype) * 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, "seed": self.seed, "name": self.name, } @keras_export("keras.optimizers.schedules.serialize") def serialize(learning_rate_schedule): """Serializes a `LearningRateSchedule` into a JSON-compatible representation. Args: learning_rate_schedule: The `LearningRateSchedule` object to serialize. Returns: A JSON-serializable dict representing the object's config. Example: >>> lr_schedule = tf.keras.optimizers.schedules.ExponentialDecay( ... 0.1, decay_steps=100000, decay_rate=0.96, staircase=True) >>> tf.keras.optimizers.schedules.serialize(lr_schedule) {'class_name': 'ExponentialDecay', 'config': {...}} """ return generic_utils.serialize_keras_object(learning_rate_schedule) @keras_export("keras.optimizers.schedules.deserialize") def deserialize(config, custom_objects=None): """Instantiates a `LearningRateSchedule` object from a serialized form. Args: config: The serialized form of the `LearningRateSchedule`. Dictionary of the form {'class_name': str, 'config': dict}. custom_objects: A dictionary mapping class names (or function names) of custom (non-Keras) objects to class/functions. Returns: A `LearningRateSchedule` object. Example: ```python # Configuration for PolynomialDecay config = { 'class_name': 'PolynomialDecay', 'config': {'cycle': False, 'decay_steps': 10000, 'end_learning_rate': 0.01, 'initial_learning_rate': 0.1, 'name': None, 'power': 0.5}} lr_schedule = tf.keras.optimizers.schedules.deserialize(config) ``` """ return generic_utils.deserialize_keras_object( config, module_objects=globals(), custom_objects=custom_objects, printable_module_name="decay", )