A Dual Approach for Optimal Algorithms in Distributed Optimization over Networks

Cesar A. Uribe, Soomin Lee, Alexander Gasnikov, Angelia Nedic

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

Abstract

We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum i = 1m fi(z) of functions over in a network. We provide complexity bounds for four different cases, namely: each function fi is strongly convex and smooth, each function is either strongly convex or smooth, and when it is convex but neither strongly convex nor smooth. Our approach is based on the dual of an appropriately formulated primal problem, which includes a graph that models the communication restrictions. We propose distributed algorithms that achieve the same optimal rates as their centralized counterparts (up to constant and logarithmic factors), with an additional optimal cost related to the spectral properties of the network. Initially, we focus on functions for which we can explicitly minimize its Legendre-Fenchel conjugate, i.e., admissible or dual friendly functions. Then, we study distributed optimization algorithms for non-dual friendly functions, as well as a method to improve the dependency on the parameters of the functions involved. Numerical analysis of the proposed algorithms is also provided.

Original languageEnglish (US)
Title of host publication2020 Information Theory and Applications Workshop, ITA 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728141909
DOIs
StatePublished - Feb 2 2020
Event2020 Information Theory and Applications Workshop, ITA 2020 - San Diego, United States
Duration: Feb 2 2020Feb 7 2020

Publication series

Name2020 Information Theory and Applications Workshop, ITA 2020

Conference

Conference2020 Information Theory and Applications Workshop, ITA 2020
CountryUnited States
CitySan Diego
Period2/2/202/7/20

Keywords

  • convex optimization
  • Distributed optimization
  • optimal rates
  • optimization over networks
  • primal-dual algorithms

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Computer Science Applications
  • Information Systems and Management
  • Control and Optimization

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