A Stochastic Variance Reduction Algorithm with Bregman Distances for Structured Composite Problems

TL;DR

This paper introduces a stochastic primal-dual splitting algorithm utilizing Bregman distances for structured composite problems, achieving sublinear convergence generally and linear convergence under strong convexity assumptions.

Contribution

It presents a novel stochastic primal-dual method with Bregman distances tailored for structured composite problems, with proven convergence rates.

Findings

Sublinear convergence in expectation of the primal-dual gap.

Linear convergence rate under strong convexity conditions.

Applicable to non-Euclidean spaces with infimal convolutions.

Abstract

We develop a novel stochastic primal dual splitting method with Bregman distances for solving a structured composite problems involving infimal convolutions in non-Euclidean spaces. The sublinear convergence in expectation of the primal-dual gap is proved under mild conditions on stepsize for the general case. The linear convergence rate is obtained under additional condition like the strong convexity relative to Bregman functions.