learning_rate_scheduler.py

# 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 . 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

__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.
    """
    global_step = _decay_step_counter(1)

    a = global_step**-0.5
    b = (warmup_steps**-1.5) * global_step
    lr_value = (d_model**-0.5) * ops.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)

    """
    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
    """
    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)
    """
    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
    """
    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 = ops.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.


    """

    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.

    ```python
        learning_rate *= local_gw_ratio * sqrt(sumsq(param))
                        / (sqrt(sumsq(gradient))+ weight_decay * sqrt(sumsq(param)))
    ```

    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
    """

    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:
        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