Source code for pennylane.optimize.rms_prop

# Copyright 2018-2021 Xanadu Quantum Technologies Inc.

# 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.
"""Root mean square propagation optimizer"""
from numpy import sqrt

from .adagrad import AdagradOptimizer


class RMSPropOptimizer(AdagradOptimizer):
    r"""Root mean squared propagation optimizer.

    The root mean square propagation optimizer is a modified
    :class:`Adagrad optimizer <pennylane.optimize.AdagradOptimizer>`,
    with a decay of learning rate adaptation.

    Extensions of the Adagrad optimization method generally
    start the sum :math:`a` over past gradients in the denominator
    of the learning rate at a finite :math:`t'` with :math:`0 < t' < t`,
    or decay past gradients to avoid an ever-decreasing learning rate.

    Root Mean Square propagation is such an adaptation, where

    .. math::
        a_i^{(t+1)} = \gamma a_i^{(t)} + (1-\gamma) (\partial_{x_i} f(x^{(t)}))^2.

    Args:
        stepsize (float): the user-defined hyperparameter :math:`\eta`
            used in the Adagrad optimization
        decay (float): the learning rate decay :math:`\gamma`
        eps (float): offset :math:`\epsilon` added for numerical stability
            (see :class:`Adagrad <pennylane.optimize.AdagradOptimizer>`)

    """

    def __init__(self, stepsize=0.01, decay=0.9, eps=1e-8):
        super().__init__(stepsize)
        self.decay = decay
        self.eps = eps

    def apply_grad(self, grad, args):
        r"""Update the variables args to take a single optimization step. Flattens and unflattens
        the inputs to maintain nested iterables as the parameters of the optimization.

        Args:
            grad (tuple [array]): the gradient of the objective function at
                point :math:`x^{(t)}`: :math:`\nabla f(x^{(t)})`.
            args (tuple): the current value of the variables :math:`x^{(t)}`.

        Returns:
            list [array]: the new values :math:`x^{(t+1)}`
        """
        args_new = list(args)

        if self.accumulation is None:
            self.accumulation = [0.0] * len(args)

        trained_index = 0
        for index, arg in enumerate(args):
            if getattr(arg, "requires_grad", False):
                self._update_accumulation(index, grad[trained_index])
                args_new[index] = (
                    arg
                    - (self.stepsize / sqrt(self.accumulation[index] + self.eps))
                    * grad[trained_index]
                )
                trained_index += 1

        return args_new

    def _update_accumulation(self, index, grad):
        r"""Update the accumulation with the gradient.

        Args:
            index (int): index of argument to update.
            grad (ndarray): gradient at the index.
        """
        self.accumulation[index] = (
            self.decay * self.accumulation[index] + (1 - self.decay) * grad**2
        )

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