Stochastic forward-backward-half forward splitting algorithm with variance reduction

TL;DR

This paper introduces a stochastic splitting algorithm with variance reduction for structured monotone inclusion problems, proving convergence and demonstrating its effectiveness through numerical experiments.

Contribution

The paper proposes a novel stochastic forward-backward-half forward splitting algorithm with variance reduction, achieving convergence guarantees for complex monotone inclusion problems.

Findings

Proven weak almost sure convergence of the algorithm.

Achieved linear convergence under strong monotonicity.

Numerical results demonstrate improved performance.

Abstract

In this paper, we present a stochastic forward-backward-half forward splitting algorithm with variance reduction for solving the structured monotone inclusion problem composed of a maximally monotone operator, a maximally monotone operator and a cocoercive operator in a separable real Hilbert space. By deffining a Lyapunov function, we establish the weak almost sure convergence of the proposed algorithm, and obtain the linear convergence when one of the maximally monotone operators is strongly monotone. Numerical examples are provided to show the performance of the proposed algorithm.