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learning_rate_scheduler.py
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learning_rate_scheduler.py
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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.
"""
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.
"""
from __future__ import print_function
import math
import numbers
from . import control_flow
from . import nn
from . import ops
from . import tensor
from ..framework import default_main_program, Parameter, unique_name, name_scope
from ..framework import Variable
from ..framework import in_dygraph_mode
from ..dygraph import learning_rate_scheduler as imperate_lr
from ..data_feeder import check_variable_and_dtype, check_type
__all__ = [
'exponential_decay', 'natural_exp_decay', 'inverse_time_decay',
'polynomial_decay', 'piecewise_decay', 'noam_decay', 'cosine_decay',
'linear_lr_warmup'
]
def _decay_step_counter(begin=0):
# the first global step is zero in learning rate decay
global_step = nn.autoincreased_step_counter(
counter_name='@LR_DECAY_COUNTER@', begin=begin, step=1)
global_step = tensor.cast(global_step, 'float32')
return global_step
def noam_decay(d_model, warmup_steps, learning_rate=1.0):
"""
Noam decay method. The numpy implementation of noam decay as follows.
.. code-block:: python
import paddle.fluid as fluid
import numpy as np
# set hyper parameters
base_lr = 0.01
d_model = 2
current_steps = 20
warmup_steps = 200
# compute
lr_value = base_lr * np.power(d_model, -0.5) * np.min([
np.power(current_steps, -0.5),
np.power(warmup_steps, -1.5) * current_steps])
Please reference `attention is all you need
<https://arxiv.org/pdf/1706.03762.pdf>`_.
Args:
d_model(Variable): The dimensionality of input and output of model.
warmup_steps(Variable): A super parameter.
learning_rate(Variable|float|int): The initial learning rate. If the type
is Variable, it's a tensor with shape [1], the data type can be
float32 or float64. It also can be set to python int number. Default 1.0
Returns:
The decayed learning rate.
Examples:
.. code-block:: python
import paddle.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,
learning_rate)
"""
with default_main_program()._lr_schedule_guard():
if in_dygraph_mode():
decay = imperate_lr.NoamDecay(
d_model, warmup_steps, learning_rate=learning_rate)
return decay
else:
global_step = _decay_step_counter(1)
a = global_step**-0.5
b = (warmup_steps**-1.5) * global_step
lr_value = learning_rate * (d_model**-0.5) * nn.elementwise_min(a,
b)
return lr_value
def exponential_decay(learning_rate, decay_steps, decay_rate, staircase=False):
"""
Applies exponential decay to the learning rate.
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
'decay_rate' every 'decay_steps' steps.
Decayed learning rate calculates as follows:
>>> 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)
Args:
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
Returns:
Variable: The decayed learning rate. The data type is float32.
Examples:
.. code-block:: python
import paddle.fluid as fluid
import paddle
paddle.enable_static()
base_lr = 0.1
sgd_optimizer = fluid.optimizer.SGD(
learning_rate=fluid.layers.exponential_decay(
learning_rate=base_lr,
decay_steps=10000,
decay_rate=0.5,
staircase=True))
"""
with default_main_program()._lr_schedule_guard():
if in_dygraph_mode():
decay = imperate_lr.ExponentialDecay(learning_rate, decay_steps,
decay_rate, staircase)
return decay
else:
global_step = _decay_step_counter()
div_res = global_step / decay_steps
if staircase:
div_res = ops.floor(div_res)
decayed_lr = learning_rate * (decay_rate**div_res)
return decayed_lr
def natural_exp_decay(learning_rate, decay_steps, decay_rate, staircase=False):
"""
Applies natural exponential decay to the initial learning rate.
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 calculates as follows:
>>> if not staircase:
>>> decayed_learning_rate = learning_rate * exp(- decay_rate * (global_step / decay_steps))
>>> else:
>>> decayed_learning_rate = learning_rate * exp(- decay_rate * floor(global_step / decay_steps))
Args:
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 natural exponential power
`decay_rate` every `decay_steps`. If False, learning rate will be
decayed continuously and following the formula above. Default: False
Returns:
The decayed learning rate. The data type is float32.
Examples:
.. code-block:: python
import paddle.fluid as fluid
import paddle
paddle.enable_static()
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))
"""
with default_main_program()._lr_schedule_guard():
if in_dygraph_mode():
decay = imperate_lr.NaturalExpDecay(learning_rate, decay_steps,
decay_rate, staircase)
return decay
else:
global_step = _decay_step_counter()
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)
return decayed_lr
def inverse_time_decay(learning_rate, decay_steps, decay_rate, staircase=False):
"""
Applies inverse time decay to the initial learning rate.
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
applied to the initial learning rate.
Decayed learning rate calculates as follows:
>>> if staircase == True:
>>> 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)
Args:
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
Returns:
Variable: The decayed learning rate. The data type is float32.
Examples:
.. code-block:: python
import paddle.fluid as fluid
import paddle
paddle.enable_static()
base_lr = 0.1
sgd_optimizer = fluid.optimizer.SGD(
learning_rate=fluid.layers.inverse_time_decay(
learning_rate=base_lr,
decay_steps=10000,
decay_rate=0.5,
staircase=True))
"""
with default_main_program()._lr_schedule_guard():
if in_dygraph_mode():
decay = imperate_lr.InverseTimeDecay(learning_rate, decay_steps,
decay_rate, staircase)
return decay
else:
global_step = _decay_step_counter()
div_res = global_step / decay_steps
if staircase:
div_res = ops.floor(div_res)
decayed_lr = learning_rate / (1 + decay_rate * div_res)
return decayed_lr
def polynomial_decay(learning_rate,
decay_steps,
end_learning_rate=0.0001,
power=1.0,
cycle=False):
"""
Applies polynomial decay to the initial learning rate.
.. code-block:: text
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
Args:
learning_rate(Variable|float32): A scalar float32 value or a Variable. This
will be the initial learning rate during training.
decay_steps(int32): A Python `int32` number.
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.
Returns:
Variable: The decayed learning rate
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)
"""
with default_main_program()._lr_schedule_guard():
if in_dygraph_mode():
decay = imperate_lr.PolynomialDecay(learning_rate, decay_steps,
end_learning_rate, power, cycle)
return decay
else:
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)
decayed_lr = (learning_rate - end_learning_rate) * \
((1 - global_step / decay_steps) ** power) + end_learning_rate
return decayed_lr
def piecewise_decay(boundaries, values):
"""
Applies piecewise decay to the initial learning rate.
The algorithm can be described as the code below.
.. code-block:: text
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
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.
Examples:
.. code-block:: python
import paddle.fluid as fluid
import paddle
paddle.enable_static()
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))
"""
with default_main_program()._lr_schedule_guard():
if len(values) - len(boundaries) != 1:
raise ValueError("len(values) - len(boundaries) should be 1")
if in_dygraph_mode():
decay = imperate_lr.PiecewiseDecay(boundaries, values, 0)
return decay
else:
global_step = _decay_step_counter()
lr = tensor.create_global_var(
shape=[1],
value=0.0,
dtype='float32',
persistable=True,
name="learning_rate")
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)
with switch.case(global_step < boundary_val):
tensor.fill_constant(
shape=[1],
dtype="float32",
value=float(values[i]),
out=lr)
with switch.default():
tensor.fill_constant(
shape=[1],
dtype="float32",
value=float(values[len(values) - 1]),
out=lr)
return lr
def cosine_decay(learning_rate, step_each_epoch, epochs):
r"""
Applies cosine decay to the learning rate.
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
following cosine decay strategy.
.. math::
decayed\_lr = learning\_rate * 0.5 * (math.cos * (epoch * \\frac{math.pi}{epochs} ) + 1)
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.
Returns:
Variable: The decayed learning rate.
Examples:
.. code-block:: python
import paddle.fluid as fluid
base_lr = 0.1
lr = fluid.layers.cosine_decay(
learning_rate = base_lr, step_each_epoch=10000, epochs=120)
"""
check_type(learning_rate, 'learning_rate', (float, tensor.Variable),
'cosine_decay')
with default_main_program()._lr_schedule_guard():
if in_dygraph_mode():
decay = imperate_lr.CosineDecay(learning_rate, step_each_epoch,
epochs)
return decay
else:
global_step = _decay_step_counter()
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
def linear_lr_warmup(learning_rate, warmup_steps, start_lr, end_lr):
"""
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.
Args:
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.
Returns:
Variable: Warm-up learning rate with the same data type as learning_rate.
Examples:
.. 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]
"""
dtype = 'float32'
if isinstance(learning_rate, Variable):
dtype = learning_rate.dtype
linear_step = float(end_lr) - float(start_lr)
with default_main_program()._lr_schedule_guard():
if in_dygraph_mode():
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