An Enhanced Gradient-Tracking Bound for Distributed Online Stochastic Convex Optimization

TL;DR

This paper improves the theoretical understanding of gradient-tracking methods in decentralized stochastic convex optimization, providing tighter convergence rates and an alternative analysis approach for static graphs.

Contribution

It introduces an enhanced analysis framework for GT methods, resulting in better network-dependent convergence rates in online stochastic convex settings.

Findings

Established tighter network-dependent rates for GT methods.

Proposed an alternative analysis approach for convex problems.

Demonstrated improved theoretical bounds over previous analyses.

Abstract

Gradient-tracking (GT) based decentralized methods have emerged as an effective and viable alternative method to decentralized (stochastic) gradient descent (DSGD) when solving distributed online stochastic optimization problems. Initial studies of GT methods implied that GT methods have worse network dependent rate than DSGD, contradicting experimental results. This dilemma has recently been resolved, and tighter rates for GT methods have been established, which improves upon DSGD. In this work, we establish more enhanced rates for GT methods under the online stochastic convex settings. We present an alternative approach for analyzing GT methods for convex problems and over static graphs. When compared to previous analyses, this approach allows us to establish enhanced network dependent rates.