Source code for pennylane.optimize.adagrad

# Copyright 2018-2020 Xanadu Quantum Technologies Inc.

# Licensed under the Apache License, Version 2.0 (the "License");
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"""Adagrad optimizer"""
import math

from pennylane.utils import _flatten, unflatten
from .gradient_descent import GradientDescentOptimizer

[docs]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 """ def __init__(self, stepsize=0.01, eps=1e-8): super().__init__(stepsize) self.eps = eps self.accumulation = None
[docs] def apply_grad(self, grad, x): r"""Update the variables x to take a single optimization step. Flattens and unflattens the inputs to maintain nested iterables as the parameters of the optimization. Args: grad (array): The gradient of the objective function at point :math:`x^{(t)}`: :math:`\nabla f(x^{(t)})` x (array): the current value of the variables :math:`x^{(t)}` Returns: array: the new values :math:`x^{(t+1)}` """ x_flat = _flatten(x) grad_flat = list(_flatten(grad)) if self.accumulation is None: self.accumulation = [g * g for g in grad_flat] else: self.accumulation = [a + g * g for a, g in zip(self.accumulation, grad_flat)] x_new_flat = [ e - (self._stepsize / math.sqrt(a + self.eps)) * g for a, g, e in zip(self.accumulation, grad_flat, x_flat) ] return unflatten(x_new_flat, x)
[docs] def reset(self): """Reset optimizer by erasing memory of past steps.""" self.accumulation = None