Proximal random reshuffling under local Lipschitz continuity

TL;DR

This paper investigates proximal random reshuffling algorithms for optimizing sums of locally Lipschitz functions combined with convex functions, providing new convergence guarantees without requiring coercivity or limit points.

Contribution

It introduces a novel analysis framework that handles conservative fields with unbounded values, extending convergence guarantees for proximal random reshuffling.

Findings

Provides convergence guarantees without coercivity assumptions

Introduces a new tracking lemma linking iterates to conservative field trajectories

Handles conservative fields with unbounded values

Abstract

We study proximal random reshuffling for minimizing the sum of locally Lipschitz functions and a proper lower semicontinuous convex function without assuming coercivity or the existence of limit points. The algorithmic guarantees pertaining to near approximate stationarity rely on a new tracking lemma linking the iterates to trajectories of conservative fields. One of the novelties in the analysis consists in handling conservative fields with unbounded values.