Source code for pennylane.optimize.rms_prop

# Copyright 2018-2021 Xanadu Quantum Technologies Inc.

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

from .adagrad import AdagradOptimizer

[docs]class RMSPropOptimizer(AdagradOptimizer): r"""Root mean squared propagation optimizer. The root mean square progation optimizer is a modified :class:`Adagrad optimizer <pennylane.optmimize.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 optmization decay (float): the learning rate decay :math:`\gamma` eps (float): offset :math:`\epsilon` added for numerical stability (see :class:`Adagrad <pennylane.optmimize.AdagradOptimizer>`) """ def __init__(self, stepsize=0.01, decay=0.9, eps=1e-8): super().__init__(stepsize) self.decay = decay self.eps = eps
[docs] 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 )