Convergence of the Iterates of the Stochastic Proximal Gradient Method

TL;DR

This paper establishes almost sure and mean convergence of the stochastic proximal gradient method for convex optimization without variance control assumptions, with applications to classification and feasibility problems.

Contribution

It provides the first convergence analysis of the stochastic proximal gradient method under minimal assumptions, including almost sure convergence.

Findings

Proves almost sure convergence of the method.

Establishes convergence in the mean.

Applies results to classification and convex feasibility problems.

Abstract

We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without requiring any boundedness or control of the variance of the random variables, we derive the almost sure convergence and the convergence in the mean of the iterates to a solution of the minimization problem. The results are applied to classification and convex feasibility problems.