Achieving Linear Convergence in Distributed Asynchronous Multiagent Optimization

Ye Tian, Ying Sun, Gesualdo Scutari

Research output: Contribution to journalArticlepeer-review

Abstract

This article studies multiagent (convex and nonconvex) optimization over static digraphs. We propose a general distributed asynchronous algorithmic framework whereby 1) agents can update their local variables as well as communicate with their neighbors at any time, without any form of coordination; and 2) they can perform their local computations using (possibly) delayed, out-of-sync information from the other agents. Delays need not be known to the agent or obey any specific profile, and can also be time-varying (but bounded). The algorithm builds on a tracking mechanism that is robust against asynchrony (in the above sense), whose goal is to estimate locally the average of agents' gradients. When applied to strongly convex functions, we prove that it converges at an R-linear (geometric) rate as long as the step-size is sufficiently small. A sublinear convergence rate is proved, when nonconvex problems and/or diminishing, uncoordinated step-sizes are considered. To the best of our knowledge, this is the first distributed algorithm with provable geometric convergence rate in such a general asynchronous setting. Preliminary numerical results demonstrate the efficacy of the proposed algorithm and validate our theoretical findings.

Original languageEnglish (US)
Article number9023394
Pages (from-to)5264-5279
Number of pages16
JournalIEEE Transactions on Automatic Control
Volume65
Issue number12
DOIs
StatePublished - Dec 2020

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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