learning_rate_scheduler.py 19.6 KB
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# Copyright (c) 2016 PaddlePaddle 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.
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"""
When training a model, it's often useful to decay the
learning rate during training process, this is called
learning_rate_decay. There are many strategies to do
this, this module will provide some classical method.
User can also implement their own learning_rate_decay
strategy according to this module.
"""
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from __future__ import print_function

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import math
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import numbers
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from . import control_flow
from . import nn
from . import ops
from . import tensor
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from ..initializer import init_on_cpu
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from ..framework import default_main_program, Parameter, unique_name, name_scope
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from ..framework import Variable
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from ..dygraph import base as imperative_base
from ..dygraph import learning_rate_scheduler as imperate_lr
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__all__ = [
    'exponential_decay', 'natural_exp_decay', 'inverse_time_decay',
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    'polynomial_decay', 'piecewise_decay', 'noam_decay', 'cosine_decay',
    'linear_lr_warmup'
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]
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def _decay_step_counter(begin=0):
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    # the first global step is zero in learning rate decay
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    global_step = nn.autoincreased_step_counter(
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        counter_name='@LR_DECAY_COUNTER@', begin=begin, step=1)
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    global_step = tensor.cast(global_step, 'float32')
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    return global_step


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def noam_decay(d_model, warmup_steps):
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    """
    Noam decay method. The numpy implementation of noam decay as follows.

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    .. code-block:: python
      
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      import padde.fluid as fluid
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      import numpy as np
      # set hyper parameters
      d_model = 2
      current_steps = 20
      warmup_steps = 200
      # compute
      lr_value = np.power(d_model, -0.5) * np.min([
                              np.power(current_steps, -0.5),
                              np.power(warmup_steps, -1.5) * current_steps])
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    Please reference `attention is all you need
    <https://arxiv.org/pdf/1706.03762.pdf>`_.
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    Args:
        d_model(Variable): The dimensionality of input and output of model.
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        warmup_steps(Variable): A super parameter.

    Returns:
        The decayed learning rate.
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    Examples:
        .. code-block:: python

          import padde.fluid as fluid
          warmup_steps = 100
          learning_rate = 0.01
          lr = fluid.layers.learning_rate_scheduler.noam_decay(
                         1/(warmup_steps *(learning_rate ** 2)),
                         warmup_steps)
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    """
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    with default_main_program()._lr_schedule_guard():
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        if imperative_base.enabled():
            decay = imperate_lr.NoamDecay(d_model, warmup_steps)
            return decay
        else:
            global_step = _decay_step_counter(1)
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            a = global_step**-0.5
            b = (warmup_steps**-1.5) * global_step
            lr_value = (d_model**-0.5) * nn.elementwise_min(a, b)
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            return lr_value
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def exponential_decay(learning_rate, decay_steps, decay_rate, staircase=False):
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    """
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    Applies exponential decay to the learning rate.
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    When training a model, it is often recommended to lower the learning rate as the
    training progresses. By using this function, the learning rate will be decayed by
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    'decay_rate' every 'decay_steps' steps.

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    Decayed learning rate calcualtes as follows:

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    >>> if staircase == True:
    >>>     decayed_learning_rate = learning_rate * decay_rate ^ floor(global_step / decay_steps)
    >>> else:
    >>>     decayed_learning_rate = learning_rate * decay_rate ^ (global_step / decay_steps)
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    Args:
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        learning_rate(Variable|float): The initial learning rate. It should be a Variable 
                                       or a float
        decay_steps(int): The learning rate decay steps. See the decay computation above.
        decay_rate(float): The learning rate decay rate. See the decay computation above.
        staircase(bool): If True, decay the learning rate at discrete intervals, which 
                         means the learning rate will be decayed by `decay_rate` every
                         `decay_steps`. If False, learning rate will be decayed continuously
                         and following the formula above. Default: False
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    Returns:
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        Variable: The decayed learning rate. The data type is float32.
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    Examples:
        .. code-block:: python

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          import paddle.fluid as fluid
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          base_lr = 0.1
          sgd_optimizer = fluid.optimizer.SGD(
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	      learning_rate=fluid.layers.exponential_decay(
		    learning_rate=base_lr,
		    decay_steps=10000,
		    decay_rate=0.5,
		    staircase=True))
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    """
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    with default_main_program()._lr_schedule_guard():
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        if imperative_base.enabled():
            decay = imperate_lr.ExponentialDecay(learning_rate, decay_steps,
                                                 decay_rate, staircase)
            return decay
        else:
            global_step = _decay_step_counter()
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            div_res = global_step / decay_steps
            if staircase:
                div_res = ops.floor(div_res)
            decayed_lr = learning_rate * (decay_rate**div_res)
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            return decayed_lr
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def natural_exp_decay(learning_rate, decay_steps, decay_rate, staircase=False):
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    """Applies natural exponential decay to the initial learning rate.

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    When training a model, it is often recommended to lower the learning rate as the
    training progresses. By using this function, the learning rate will be decayed by
    natural exponential power 'decay_rate' every 'decay_steps' steps.

    Decayed learning rate calcualtes as follows:

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    >>> if not staircase:
    >>>     decayed_learning_rate = learning_rate * exp(- decay_rate * (global_step / decay_steps))
    >>> else:
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    >>>     decayed_learning_rate = learning_rate * exp(- decay_rate * floor(global_step / decay_steps))
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    Args:
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        learning_rate(Variable|float): The initial learning rate. It should be a Variable 
                                       or a float
        decay_steps(int): The learning rate decay steps. See the decay computation above.
        decay_rate(float): The learning rate decay rate. See the decay computation above.
        staircase(bool): If True, decay the learning rate at discrete intervals, which 
                         means the learning rate will be decayed by natual exponential power
                         `decay_rate` every `decay_steps`. If False, learning rate will be
                         decayed continuously and following the formula above. Default: False
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    Returns:
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        The decayed learning rate. The data type is float32.
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    Examples:
        .. code-block:: python

          import paddle.fluid as fluid
          base_lr = 0.1
          sgd_optimizer = fluid.optimizer.SGD(
	      learning_rate=fluid.layers.natural_exp_decay(
		    learning_rate=base_lr,
		    decay_steps=10000,
		    decay_rate=0.5,
		    staircase=True))

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    """
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    with default_main_program()._lr_schedule_guard():
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        if imperative_base.enabled():
            decay = imperate_lr.NaturalExpDecay(learning_rate, decay_steps,
                                                decay_rate, staircase)
            return decay
        else:
            global_step = _decay_step_counter()
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            div_res = global_step / decay_steps
            if staircase:
                div_res = ops.floor(div_res)
            decayed_lr = learning_rate * ops.exp(-1 * decay_rate * div_res)
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            return decayed_lr
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def inverse_time_decay(learning_rate, decay_steps, decay_rate, staircase=False):
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    """
    Applies inverse time decay to the initial learning rate.
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    When training a model, it is often recommended to lower the learning rate as the
    training progresses. By using this function, an inverse decay function will be
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    applied to the initial learning rate.
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    Decayed learning rate calcualtes as follows:

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    >>> if staircase == True:
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    >>>     decayed_learning_rate = learning_rate / (1 + decay_rate * floor(global_step / decay_step))
    >>> else:
    >>>     decayed_learning_rate = learning_rate / (1 + decay_rate * global_step / decay_step)

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    Args:
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        learning_rate(Variable|float): The initial learning rate. It should be a Variable 
                                       or a float
        decay_steps(int): The learning rate decay steps. See the decay computation above.
        decay_rate(float): The learning rate decay rate. See the decay computation above.
        staircase(bool): If True, decay the learning rate at discrete intervals, which 
                         means the learning rate will be decayed by `decay_rate` times 
                         every `decay_steps`. If False, learning rate will be decayed 
                         continuously and following the formula above. Default: False
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    Returns:
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        Variable: The decayed learning rate. The data type is float32.
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    Examples:
        .. code-block:: python

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          import paddle.fluid as fluid
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          base_lr = 0.1
          sgd_optimizer = fluid.optimizer.SGD(
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	      learning_rate=fluid.layers.inverse_time_decay(
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		    learning_rate=base_lr,
		    decay_steps=10000,
		    decay_rate=0.5,
		    staircase=True))
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    """
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    with default_main_program()._lr_schedule_guard():
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        if imperative_base.enabled():
            decay = imperate_lr.InverseTimeDecay(learning_rate, decay_steps,
                                                 decay_rate, staircase)
            return decay
        else:
            global_step = _decay_step_counter()
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            div_res = global_step / decay_steps
            if staircase:
                div_res = ops.floor(div_res)
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            decayed_lr = learning_rate / (1 + decay_rate * div_res)
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            return decayed_lr
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def polynomial_decay(learning_rate,
                     decay_steps,
                     end_learning_rate=0.0001,
                     power=1.0,
                     cycle=False):
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    """
    Applies polynomial decay to the initial learning rate.

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    .. code-block:: text
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     if cycle:
       decay_steps = decay_steps * ceil(global_step / decay_steps)
     else:
       global_step = min(global_step, decay_steps)
       decayed_learning_rate = (learning_rate - end_learning_rate) *
            (1 - global_step / decay_steps) ^ power + end_learning_rate
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    Args:
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        learning_rate(Variable|float32): A scalar float32 value or a Variable. This
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          will be the initial learning rate during training.
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        decay_steps(int32): A Python `int32` number.
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        end_learning_rate(float): A Python `float` number.
        power(float): A Python `float` number.
        cycle(bool): If set true, decay the learning rate every decay_steps.
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    Returns:
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        Variable: The decayed learning rate
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    Examples:
        .. code-block:: python

          import paddle.fluid as fluid
          start_lr = 0.01
          total_step = 5000
          end_lr = 0
          lr = fluid.layers.polynomial_decay(
              start_lr, total_step, end_lr, power=1)

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    """
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    with default_main_program()._lr_schedule_guard():
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        if imperative_base.enabled():
            decay = imperate_lr.PolynomialDecay(learning_rate, decay_steps,
                                                end_learning_rate, power, cycle)
            return decay
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        else:
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            global_step = _decay_step_counter()

            if cycle:
                div_res = ops.ceil(global_step / decay_steps)
                zero_var = tensor.fill_constant(
                    shape=[1], dtype='float32', value=0.0)
                one_var = tensor.fill_constant(
                    shape=[1], dtype='float32', value=1.0)

                with control_flow.Switch() as switch:
                    with switch.case(global_step == zero_var):
                        tensor.assign(input=one_var, output=div_res)
                decay_steps = decay_steps * div_res
            else:
                decay_steps_var = tensor.fill_constant(
                    shape=[1], dtype='float32', value=float(decay_steps))
                global_step = nn.elementwise_min(
                    x=global_step, y=decay_steps_var)
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            decayed_lr = (learning_rate - end_learning_rate) * \
                ((1 - global_step / decay_steps) ** power) + end_learning_rate
            return decayed_lr
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def piecewise_decay(boundaries, values):
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    """Applies piecewise decay to the initial learning rate.

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    The algorithm can be described as the code below.
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    .. code-block:: text
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      boundaries = [10000, 20000]
      values = [1.0, 0.5, 0.1]
      if step < 10000:
          learning_rate = 1.0
      elif 10000 <= step < 20000:
          learning_rate = 0.5
      else:
          learning_rate = 0.1
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    Args:
        boundaries: A list of steps numbers.
        values: A list of learning rate values that will be picked during
            different step boundaries.

    Returns:
        The decayed learning rate.

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    Examples:
        .. code-block:: python

          import paddle.fluid as fluid
          boundaries = [10000, 20000]
          values = [1.0, 0.5, 0.1]
          optimizer = fluid.optimizer.Momentum(
              momentum=0.9,
              learning_rate=fluid.layers.piecewise_decay(boundaries=boundaries, values=values),
              regularization=fluid.regularizer.L2Decay(1e-4))

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    """
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    with default_main_program()._lr_schedule_guard():
        if len(values) - len(boundaries) != 1:
            raise ValueError("len(values) - len(boundaries) should be 1")

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        if imperative_base.enabled():
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            decay = imperate_lr.PiecewiseDecay(boundaries, values, 0)
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            return decay
        else:
            global_step = _decay_step_counter()
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            lr = tensor.create_global_var(
                shape=[1],
                value=0.0,
                dtype='float32',
                persistable=True,
                name="learning_rate")
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            with control_flow.Switch() as switch:
                for i in range(len(boundaries)):
                    boundary_val = tensor.fill_constant(
                        shape=[1],
                        dtype='float32',
                        value=float(boundaries[i]),
                        force_cpu=True)
                    value_var = tensor.fill_constant(
                        shape=[1], dtype='float32', value=float(values[i]))
                    with switch.case(global_step < boundary_val):
                        tensor.assign(value_var, lr)
                last_value_var = tensor.fill_constant(
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                    shape=[1],
                    dtype='float32',
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                    value=float(values[len(values) - 1]))
                with switch.default():
                    tensor.assign(last_value_var, lr)
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            return lr
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def cosine_decay(learning_rate, step_each_epoch, epochs):
    """
    Applies cosine decay to the learning rate.

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    when training a model, it is often recommended to lower the learning rate as the
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    training progresses. By using this function, the learning rate will be decayed by
    following cosine decay strategy.
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    .. math::

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        decayed\_lr = learning\_rate * 0.5 * (math.cos * (epoch * \\frac{math.pi}{epochs} ) + 1)

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    Args:
        learning_rate(Variable|float): The initial learning rate.
        step_each_epoch(int): the number of steps in an epoch.
        epochs(int): the number of epochs.

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    Returns:
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        Variable: The decayed learning rate.
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    Examples:
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        .. code-block:: python
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            import paddle.fluid as fluid
            base_lr = 0.1
            lr = fluid.layers.cosine_decay(
            learning_rate = base_lr, step_each_epoch=10000, epochs=120)
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    """
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    with default_main_program()._lr_schedule_guard():
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        if imperative_base.enabled():
            decay = imperate_lr.CosineDecay(learning_rate, step_each_epoch,
                                            epochs)
            return decay
        else:
            global_step = _decay_step_counter()
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            cur_epoch = ops.floor(global_step / step_each_epoch)
            decayed_lr = learning_rate * 0.5 * (
                ops.cos(cur_epoch * math.pi / epochs) + 1)
            return decayed_lr
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def linear_lr_warmup(learning_rate, warmup_steps, start_lr, end_lr):
    """
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    This operator use the linear learning rate warm up strategy to adjust the learning rate preliminarily before the normal learning rate scheduling.
    For more information, please refer to `Bag of Tricks for Image Classification with Convolutional Neural Networks <https://arxiv.org/abs/1812.01187>`_
    
    When global_step < warmup_steps, learning rate is updated as:
    
    .. code-block:: text
    
            linear_step = end_lr - start_lr
            lr = start_lr + linear_step * (global_step / warmup_steps)
    
    where start_lr is the initial learning rate, and end_lr is the final learning rate;
    
    When global_step >= warmup_steps, learning rate is updated as:
    
    .. code-block:: text
    
            lr = learning_rate
    
    where lr is the learning_rate after warm-up.
    
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    Args:
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        learning_rate (Variable|float): Learning_rate after warm-up, it could be 1D-Tensor or single value with the data type of float32.
        warmup_steps (int): Steps for warm up.
        start_lr (float): Initial learning rate of warm up.
        end_lr (float): Final learning rate of warm up.
    
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    Returns:
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        Variable: Warm-up learning rate with the same data type as learning_rate.
    
    
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    Examples:
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    .. code-block:: python
    
        import paddle.fluid as fluid
    
        boundaries = [100, 200]
        lr_steps = [0.1, 0.01, 0.001]
        learning_rate = fluid.layers.piecewise_decay(boundaries, lr_steps) #case1, 1D-Tensor
        #learning_rate = 0.1  #case2, single-value
        warmup_steps = 50
        start_lr = 1. / 3.
        end_lr = 0.1
        decayed_lr = fluid.layers.linear_lr_warmup(learning_rate,
            warmup_steps, start_lr, end_lr)
    
        place = fluid.CPUPlace()
        exe = fluid.Executor(place)
        exe.run(fluid.default_startup_program())
        out, = exe.run(fetch_list=[decayed_lr.name])
        print(out)
        # case1: [0.33333334]
        # case2: [0.33333334]
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    """
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    dtype = 'float32'
    if isinstance(learning_rate, Variable):
        dtype = learning_rate.dtype

    linear_step = float(end_lr) - float(start_lr)
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    with default_main_program()._lr_schedule_guard():
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        if imperative_base.enabled():
            lr = imperate_lr.LinearLrWarmup(learning_rate, warmup_steps,
                                            start_lr, end_lr)
            return lr
        else:
            lr = tensor.create_global_var(
                shape=[1],
                value=0.0,
                dtype=dtype,
                persistable=True,
                name="learning_rate_warmup")

            global_step = _decay_step_counter()

            with control_flow.Switch() as switch:
                with switch.case(global_step < warmup_steps):
                    decayed_lr = start_lr + linear_step * (global_step /
                                                           float(warmup_steps))
                    tensor.assign(decayed_lr, lr)
                with switch.default():
                    if not isinstance(learning_rate, Variable):
                        learning_rate = tensor.fill_constant(
                            shape=[1], dtype=dtype, value=float(learning_rate))
                    tensor.assign(learning_rate, lr)
            return lr