Source code for mxnet.optimizer.nadam

# coding: utf-8
# Licensed to the Apache Software Foundation (ASF) under one
# or more contributor license agreements.  See the NOTICE file
# distributed with this work for additional information
# regarding copyright ownership.  The ASF licenses this file
# to you 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.

# pylint: disable=W0223
"""Nadam optimizer."""
from __future__ import absolute_import
from ..ndarray import (zeros, clip, sqrt, square)
from .optimizer import Optimizer, register

__all__ = ['Nadam']



[docs]@register
class Nadam(Optimizer):
    """The Nesterov Adam optimizer.

    Much like Adam is essentially RMSprop with momentum,
    Nadam is Adam RMSprop with Nesterov momentum available
    at http://cs229.stanford.edu/proj2015/054_report.pdf.

    This optimizer accepts the following parameters in addition to those accepted
    by :class:`.Optimizer`.

    Parameters
    ----------
    learning_rate : float, default 0.001
        The initial learning rate. If None, the optimization will use the
        learning rate from ``lr_scheduler``. If not None, it will overwrite
        the learning rate in ``lr_scheduler``. If None and ``lr_scheduler``
        is also None, then it will be set to 0.01 by default.
    beta1 : float, default 0.9
        Exponential decay rate for the first moment estimates.
    beta2 : float, default 0.999
        Exponential decay rate for the second moment estimates.
    epsilon : float, default 1e-8
        Small value to avoid division by 0.
    schedule_decay : float, default 0.004
        Exponential decay rate for the momentum schedule
    use_fused_step : bool, default False
        Whether or not to use fused kernels for optimizer.
        When use_fused_step=False, step is called,
        otherwise, fused_step is called.
    """
    def __init__(self, learning_rate=0.001, beta1=0.9, beta2=0.999, epsilon=1e-8,
                 schedule_decay=0.004, use_fused_step=False, **kwargs):
        super(Nadam, self).__init__(learning_rate=learning_rate,
                                    use_fused_step=use_fused_step,
                                    **kwargs)
        self.beta1 = beta1
        self.beta2 = beta2
        self.epsilon = epsilon
        self.schedule_decay = schedule_decay
        self.m_schedule = 1.


[docs]    def create_state(self, index, weight):
        return (zeros(weight.shape, weight.context, dtype=weight.dtype),  # mean
                zeros(weight.shape, weight.context, dtype=weight.dtype))  # variance



[docs]    def step(self, indices, weights, grads, states):
        """Perform an optimization step using gradients and states.

        Parameters
        ----------
        indices : list of int
            List of unique indices of the parameters into the individual learning rates
            and weight decays. Learning rates and weight decay may be set via `set_lr_mult()`
            and `set_wd_mult()`, respectively.
        weights : list of NDArray
            List of parameters to be updated.
        grads : list of NDArray
            List of gradients of the objective with respect to this parameter.
        states : List of any obj
            List of state returned by `create_state()`.
        """
        for index, weight, grad, state in zip(indices, weights, grads, states):
            self._update_count(index)
            lr = self._get_lr(index)
            wd = self._get_wd(index)
            t = self._index_update_count[index]

            # preprocess grad
            grad *= self.rescale_grad
            if self.clip_gradient is not None:
                grad = clip(grad, -self.clip_gradient, self.clip_gradient)
            grad += wd * weight

            coef2 = 1. - self.beta2**t

            # warming momentum schedule
            momentum_t = self.beta1 * (1. - 0.5 * (pow(0.96, t * self.schedule_decay)))
            momentum_t_1 = self.beta1 * (1. - 0.5 * (pow(0.96, (t + 1) * self.schedule_decay)))
            self.m_schedule = self.m_schedule * momentum_t
            m_schedule_next = self.m_schedule * momentum_t_1

            # update mean and var
            mean, var = state
            mean[:] *= self.beta1
            mean[:] += (1. - self.beta1) * grad
            var[:] *= self.beta2
            var[:] += (1. - self.beta2) * square(grad)

            grad_prime = grad / (1. - self.m_schedule)
            mean_prime = mean / (1. - m_schedule_next)
            var_prime = var / coef2
            mean_bar = momentum_t_1 * mean_prime + (1. - momentum_t) * grad_prime

            # update weight
            d = mean_bar / (sqrt(var_prime) + self.epsilon)
            weight[:] -= lr * d