Early stopping of stochastic variance reduced gradient for linear inverse problems by the discrepancy principle

Abstract

Stochastic variance reduced gradient (SVRG) is a variant of stochastic gradient descent and is a promising iterative method for solving large-scale inverse problems. Nevertheless, the development of theoretically grounded a posteriori stopping rules for SVRG remains an open challenge. In this work, we provide a convergence analysis of SVRG equipped with the discrepancy principle, the most well-known a posteriori stopping rule, for solving a class of linear inverse problems in Hilbert spaces. We establish the regularizing property of SVRG, and moreover, under suitable source conditions, we derive convergence rates of SVRG iterates. To the best of our knowledge, these are the first convergence rate results of any stochastic iterative method for inverse problems under the a posteriori stopping rule. The theoretical findings are supported by numerical experiments.