Source code for pennylane.optimize.nesterov_momentum

# 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.
"""Nesterov momentum optimizer"""
from pennylane._grad import grad as get_gradient

from .momentum import MomentumOptimizer


class NesterovMomentumOptimizer(MomentumOptimizer):
    r"""Gradient-descent optimizer with Nesterov momentum.

    Nesterov Momentum works like the
    :class:`Momentum optimizer <.pennylane.optimize.MomentumOptimizer>`,
    but shifts the current input by the momentum term when computing the gradient
    of the objective function:

    .. math:: a^{(t+1)} = m a^{(t)} + \eta \nabla f(x^{(t)} - m a^{(t)}).

    The user defined parameters are:

    * :math:`\eta`: the step size
    * :math:`m`: the momentum

    Args:
        stepsize (float): user-defined hyperparameter :math:`\eta`
        momentum (float): user-defined hyperparameter :math:`m`

    .. note::

        When using ``torch``, ``tensorflow`` or ``jax`` interfaces, refer to :doc:`Gradients and training </introduction/interfaces>` for suitable optimizers.

    """

    def compute_grad(
        self, objective_fn, args, kwargs, grad_fn=None
    ):  # pylint: disable=arguments-renamed
        r"""Compute the gradient of the objective function at the shifted point :math:`(x -
        m\times\text{accumulation})` and return it along with the objective function forward pass
        (if available).

        Args:
            objective_fn (function): the objective function for optimization.
            args (tuple): tuple of NumPy arrays containing the current values for the
                objection function.
            kwargs (dict): keyword arguments for the objective function.
            grad_fn (function): optional gradient function of the objective function with respect to
                the variables ``x``. If ``None``, the gradient function is computed automatically.
                Must return the same shape of tuple [array] as the autograd derivative.

        Returns:
            tuple [array]: the NumPy array containing the gradient :math:`\nabla f(x^{(t)})` and the
            objective function output. If ``grad_fn`` is provided, the objective function
            will not be evaluated and instead ``None`` will be returned.
        """
        shifted_args = list(args)

        trainable_indices = [
            i for i, arg in enumerate(args) if getattr(arg, "requires_grad", False)
        ]

        if self.accumulation:
            for index in trainable_indices:
                shifted_args[index] = args[index] - self.momentum * self.accumulation[index]

        g = get_gradient(objective_fn) if grad_fn is None else grad_fn
        grad = g(*shifted_args, **kwargs)
        forward = getattr(g, "forward", None)

        grad = (grad,) if len(trainable_indices) == 1 else grad
        return grad, forward

_modules/pennylane/optimize/nesterov_momentum

 

Download Python script

 

Download Notebook

 

View on GitHub