ASY-SONATA: Achieving Linear Convergence in Distributed Asynchronous Multiagent Optimization

Ye Tian, Ying Sun, Gesualdo Scutari

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This papers studies multi-agent (convex and nonconvex) optimization over static digraphs. We propose a general distributed asynchronous algorithmic framework whereby i) agents can update their local variables as well as communicate with their neighbors at any time, without any form of coordination; and ii) they can perform their local computations using (possibly) delayed, out-of-sync information from their neighbors. Delays need not be known to the agents 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 sum 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 employed. To the best of our knowledge, this is the first distributed algorithm with provable geometric convergence rate in such a general asynchonous setting.

Original languageEnglish (US)
Title of host publication2018 56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages543-551
Number of pages9
ISBN (Electronic)9781538665961
DOIs
StatePublished - Feb 5 2019
Event56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018 - Monticello, United States
Duration: Oct 2 2018Oct 5 2018

Publication series

Name2018 56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018

Conference

Conference56th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2018
CountryUnited States
CityMonticello
Period10/2/1810/5/18

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Hardware and Architecture
  • Signal Processing
  • Energy Engineering and Power Technology
  • Control and Optimization

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