Source code for pennylane.optimize.adagrad

# 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.
"""Adagrad optimizer"""
from numpy import sqrt

from .gradient_descent import GradientDescentOptimizer


class AdagradOptimizer(GradientDescentOptimizer):
    r"""Gradient-descent optimizer with past-gradient-dependent
    learning rate in each dimension.

    Adagrad adjusts the learning rate for each parameter :math:`x_i`
    in :math:`x` based on past gradients. We therefore have to consider
    each parameter update individually,

    .. math::
        x^{(t+1)}_i = x^{(t)}_i - \eta_i^{(t+1)} \partial_{w_i} f(x^{(t)}),

    where the gradient is replaced by a (scalar) partial derivative.

    The learning rate in step :math:`t` is given by

    .. math::
        \eta_i^{(t+1)} = \frac{ \eta_{\mathrm{init}} }{ \sqrt{a_i^{(t+1)} + \epsilon } },
        ~~~ a_i^{(t+1)} = \sum_{k=1}^t (\partial_{x_i} f(x^{(k)}))^2.

    The offset :math:`\epsilon` avoids division by zero.

    :math:`\eta` is the step size, a user defined parameter.

    Args:
        stepsize (float): the user-defined hyperparameter :math:`\eta`
        eps (float): offset :math:`\epsilon` added for numerical stability

    .. note::

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

    """

    def __init__(self, stepsize=0.01, eps=1e-8):
        super().__init__(stepsize)
        self.eps = eps
        self.accumulation = None

    def apply_grad(self, grad, args):
        r"""Update the variables in 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: 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])

                coeff = self.stepsize / sqrt(self.accumulation[index] + self.eps)
                args_new[index] = arg - coeff * grad[trained_index]

                trained_index += 1

        return args_new

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

        Args:
            index (int): index of parameter to update.
            grad_flat (ndarray): gradient at index
        """
        self.accumulation[index] = self.accumulation[index] + grad**2

    def reset(self):
        """Reset optimizer by erasing memory of past steps."""
        self.accumulation = None

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