An analysis of stochastic variance reduced gradient for linear inverse problems * *The work of BJ is supported by UK EPSRC Grant EP/T000864/1. The work of JZ was substantially supported by Hong Kong RGC General Research Fund (Projects 14306718 and 14306719).

Abstract

Stochastic variance reduced gradient (SVRG) is a popular variance reduction technique for accelerating stochastic gradient descent (SGD). We provide a first analysis of the method for solving a class of linear inverse problems in the lens of the classical regularization theory. We prove that for a suitable constant step size schedule, the method can achieve an optimal convergence rate in terms of the noise level (under suitable regularity condition) and the variance of the SVRG iterate error is smaller than that by SGD. These theoretical findings are corroborated by a set of numerical experiments.