Geometrically convergent distributed optimization with uncoordinated step-sizes

Angelia Nedich, Alex Olshevsky, Wei Shi, Cesar A. Uribe

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

28 Scopus citations

Abstract

A recent algorithmic family for distributed optimization, DIGing's, have been shown to have geometric convergence over time-varying undirected/directed graphs [1]. Nevertheless, an identical step-size for all agents is needed. In this paper, we study the convergence rates of the Adapt-Then-Combine (ATC) variation of the DIGing algorithm under uncoordinated step-sizes. We show that the ATC variation of DIGing algorithm converges geometrically fast even if the step-sizes are different among the agents. In addition, our analysis implies that the ATC structure can accelerate convergence compared to the distributed gradient descent (DGD) structure which has been used in the original DIGing algorithm.

Original languageEnglish (US)
Title of host publication2017 American Control Conference, ACC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3950-3955
Number of pages6
ISBN (Electronic)9781509059928
DOIs
StatePublished - Jun 29 2017
Event2017 American Control Conference, ACC 2017 - Seattle, United States
Duration: May 24 2017May 26 2017

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2017 American Control Conference, ACC 2017
CountryUnited States
CitySeattle
Period5/24/175/26/17

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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    Nedich, A., Olshevsky, A., Shi, W., & Uribe, C. A. (2017). Geometrically convergent distributed optimization with uncoordinated step-sizes. In 2017 American Control Conference, ACC 2017 (pp. 3950-3955). [7963560] (Proceedings of the American Control Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2017.7963560