Adaptive Stepsize Selection in Decentralized Convex Optimization

TL;DR

This paper presents a decentralized optimization algorithm that adaptively chooses stepsizes without global knowledge, ensuring fast convergence for convex problems and simplifying parameter tuning in multi-agent systems.

Contribution

It introduces a fully adaptive decentralized algorithm that eliminates the need for global information and prior parameter tuning, maintaining optimal convergence rates.

Findings

Converges linearly for strongly convex losses.

Achieves sublinear convergence for general convex losses.

Requires only neighbor-to-neighbor communication without global knowledge.

Abstract

We study decentralized optimization where multiple agents minimize the average of their (strongly) convex, smooth losses over a communication graph. Convergence of the existing decentralized methods generally hinges on an apriori, proper selection of the stepsize. Choosing this value is notoriously delicate: (i) it demands global knowledge from all the agents of the graph's connectivity and every local smoothness/strong-convexity constants--information they rarely have; (ii) even with perfect information, the worst-case tuning forces an overly small stepsize, slowing convergence in practice; and (iii) large-scale trial-and-error tuning is prohibitive. This work introduces a decentralized algorithm that is fully adaptive in the choice of the agents' stepsizes, without any global information and using only neighbor-to-neighbor communications--agents need not even know whether the problem is strongly convex. The algorithm retains strong guarantees: it converges at \emph{linear} rate when the losses are strongly convex and at \emph{sublinear} rate otherwise, matching the best-known rates of (nonadaptive) parameter-dependent methods.