A Unified Contraction Analysis of a Class of Distributed Algorithms for Composite Optimization

Jinming Xu, Ying Sun, Ye Tian, Gesualdo Scutari

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

2 Scopus citations

Abstract

We study distributed composite optimization over networks: agents minimize the sum of a smooth (strongly) convex function-the agents' sum-utility-plus a nonsmooth (extended-valued) convex one. We propose a general algorithmic framework for such a class of problems and provide a unified convergence analysis leveraging the theory of operator splitting. Our results unify several approaches proposed in the literature of distributed optimization for special instances of our formulation. Distinguishing features of our scheme are: (i) when the agents' functions are strongly convex, the algorithm converges at a linear rate, whose dependencies on the agents' functions and the network topology are decoupled, matching the typical rates of centralized optimization; (ii) the step-size does not depend on the network parameters but only on the optimization ones; and (iii) the algorithm can adjust the ratio between the number of communications and computations to achieve the same rate of the centralized proximal gradient scheme (in terms of computations). This is the first time that a distributed algorithm applicable to composite optimization enjoys such properties.

Original languageEnglish (US)
Title of host publication2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages485-489
Number of pages5
ISBN (Electronic)9781728155494
DOIs
StatePublished - Dec 2019
Event8th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2019 - Le Gosier, Guadeloupe
Duration: Dec 15 2019Dec 18 2019

Publication series

Name2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2019 - Proceedings

Conference

Conference8th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2019
Country/TerritoryGuadeloupe
CityLe Gosier
Period12/15/1912/18/19

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Artificial Intelligence
  • Computer Networks and Communications

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