An Analysis of Stochastic Variance Reduced Gradient for Linear Inverse Problems

TL;DR

This paper analyzes the effectiveness of SVRG for linear inverse problems, demonstrating optimal convergence rates and reduced variance compared to SGD, supported by theoretical proofs and numerical experiments.

Contribution

First analysis of SVRG for linear inverse problems showing optimal convergence and variance reduction within regularization theory.

Findings

SVRG achieves optimal convergence rate under certain conditions.

Variance of SVRG iterates is smaller than that of SGD.

Numerical experiments confirm theoretical results.

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.