A Unified Algorithmic Framework for Distributed Composite Optimization

Jinming Xu, Ye Tian, Ying Sun, Gesualdo Scutari

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

Abstract

We study distributed composite optimization over networks: agents minimize a sum of smooth (strongly) convex functions-the agents' sum-utility-plus a nonsmooth (extended-valued) convex one. We propose a general unified algorithmic framework for such a class of problems, whose unified convergence analysis leverages the theory of operator splitting. Distinguishing features of our scheme are: (i) When the agents' functions are strongly convex, the algorithm converges at a linear rate, whose dependence on the agents' functions and network topology is decoupled, matching the typical rates of centralized optimization; the rate expression improves on existing results; (ii) When the objective function is convex (but not strongly convex), similar separation as in (i) is established for the coefficient of the proved sublinear rate; and (iii) A by-product of our analysis is a tuning recommendation for several existing (non-accelerated) distributed algorithms yielding the fastest provable (worst-case) convergence rate. This is the first time that a general distributed algorithmic framework applicable to composite optimization enjoys all such properties.

Original languageEnglish (US)
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2309-2316
Number of pages8
ISBN (Electronic)9781728174471
DOIs
StatePublished - Dec 14 2020
Event59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of
Duration: Dec 14 2020Dec 18 2020

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2020-December
ISSN (Print)0743-1546

Conference

Conference59th IEEE Conference on Decision and Control, CDC 2020
CountryKorea, Republic of
CityVirtual, Jeju Island
Period12/14/2012/18/20

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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