Distributed Stochastic Nonsmooth Nonconvex Optimization

TL;DR

This paper introduces the first convergence analysis of a decentralized stochastic subgradient method tailored for nonconvex, nonsmooth, and stochastic optimization problems over fixed undirected networks, addressing a gap in theoretical understanding.

Contribution

It provides the first theoretical convergence analysis for distributed stochastic subgradient algorithms applied to nonconvex, nonsmooth, and stochastic objectives in networked settings.

Findings

Convergence guarantees for the proposed method.

Applicability to machine learning and signal processing problems.

Addresses a previously unexplored class of optimization problems.

Abstract

Distributed consensus optimization has received considerable attention in recent years; several distributed consensus-based algorithms have been proposed for (nonsmooth) convex and (smooth) nonconvex objective functions. However, the behavior of these distributed algorithms on {\it nonconvex, nonsmooth and stochastic} objective functions is not understood. This class of functions and distributed setting are motivated by several applications, including problems in machine learning and signal processing. This paper presents the first convergence analysis of the decentralized stochastic subgradient method for such classes of problems, over networks modeled as undirected, fixed, graphs.