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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
from . import control_flow
from . import nn
from . import ops
from . import tensor
from ..initializer import init_on_cpu
from ..framework import default_main_program, Parameter, unique_name, name_scope
__all__ = [
'exponential_decay', 'natural_exp_decay', 'inverse_time_decay',
'polynomial_decay', 'piecewise_decay', 'noam_decay', 'append_LARS'
]
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):
"""
Noam decay method. The numpy implementation of noam decay as follows.
>>> import numpy as np
>>> lr_value = 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.
Returns:
The decayed learning rate.
"""
with default_main_program()._lr_schedule_guard():
global_step = _decay_step_counter(1)
a = global_step**-0.5
b = (warmup_steps**-1.5) * global_step
lr_value = (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.
>>> 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.
decay_steps(int): See the decay computation above.
decay_rate(float): The decay rate. See the decay computation above.
staircase(Boolean): If True, decay the learning rate at discrete intervals.
Default: False
Returns:
Variable: The decayed learning rate
Examples:
.. code-block:: python
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))
sgd_optimizer.minimize(avg_cost)
"""
with default_main_program()._lr_schedule_guard():
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.
>>> if not staircase:
>>> decayed_learning_rate = learning_rate * exp(- decay_rate * (global_step / decay_steps))
>>> else:
>>> decayed_learning_rate = learning_rate * exp(- decay_rate * (global_step / decay_steps))
Args:
learning_rate: A scalar float32 value or a Variable. This
will be the initial learning rate during training
decay_steps: A Python `int32` number.
decay_rate: A Python `float` number.
staircase: Boolean. If set true, decay the learning rate every decay_steps.
Returns:
The decayed learning rate
"""
with default_main_program()._lr_schedule_guard():
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.
>>> 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.
decay_steps(int): See the decay computation above.
decay_rate(float): The decay rate. See the decay computation above.
staircase(Boolean): If True, decay the learning rate at discrete intervals.
Default: False
Returns:
Variable: The decayed learning rate
Examples:
.. code-block:: python
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))
sgd_optimizer.minimize(avg_cost)
"""
with default_main_program()._lr_schedule_guard():
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:: python
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
"""
with default_main_program()._lr_schedule_guard():
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:: python
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.
"""
with default_main_program()._lr_schedule_guard():
if len(values) - len(boundaries) != 1:
raise ValueError("len(values) - len(boundaries) should be 1")
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)
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(
shape=[1],
dtype='float32',
value=float(values[len(values) - 1]))
with switch.default():
tensor.assign(last_value_var, lr)
return lr
def append_LARS(params_grads, learning_rate, weight_decay):
"""
Applies LARS (LAYER-WISE ADAPTIVE RATE SCALING) to learning rate for
each layer.
Args:
learning_rate: A learning rate Variable. This
is the global learning rate for LARS.
weight_decay: A Python `float` number.
Returns:
The decayed learning rate
Examples:
.. code-block:: python
learning_rate *= local_gw_ratio * sqrt(sumsq(param))
/ (sqrt(sumsq(gradient))+ weight_decay * sqrt(sumsq(param)))
"""
def _balanced_weight(param_norm, grad_norm):
if weight_decay == 1.0:
return grad_norm + param_norm
else:
return grad_norm + weight_decay * param_norm
for param, grad in params_grads:
with param.block.program.optimized_guard(
[param, grad]), name_scope("optimizer"):
param_lr = param.optimize_attr['learning_rate']
param_norm = ops.sqrt(nn.reduce_sum(input=ops.square(param)))
grad_norm = ops.sqrt(nn.reduce_sum(input=ops.square(grad)))
if type(param_lr) == float and param_lr == 1.0:
decayed_lr = learning_rate * param_norm \
/ _balanced_weight(param_norm, grad_norm)
else:
decayed_lr = learning_rate * param_lr * param_norm \
/ _balanced_weight(param_norm, grad_norm)
# set back param local learning rate
param.optimize_attr['learning_rate'] = decayed_lr