Coordinate Dual Averaging for Decentralized Online Optimization with Nonseparable Global Objectives

Soomin Lee, Angelia Nedich, Maxim Raginsky

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider a decentralized online convex optimization problem in a network of agents, where each agent controls only a coordinate (or a part) of the global decision vector. For such a problem, we propose two decentralized variants (ODA-C and ODA-PS) of Nesterov's primal-dual algorithm with dual averaging. In ODA-C, to mitigate the disagreements on the primal-vector updates, the agents implement a generalization of the local information-exchange dynamics recently proposed by Li and Marden [1] over a static undirected graph. In ODA-PS, the agents implement the broadcast-based push-sum dynamics [2] over a time-varying sequence of uniformly connected digraphs. We show that the regret bounds in both cases have sublinear growth of O(T), with the time horizon T, when the stepsize is of the form 1t and the objective functions are Lipschitz-continuous convex functions with Lipschitz gradients. We also implement the proposed algorithms on a sensor network to complement our theoretical analysis.

Original languageEnglish (US)
Pages (from-to)34-44
Number of pages11
JournalIEEE Transactions on Control of Network Systems
Volume5
Issue number1
DOIs
StatePublished - Mar 1 2018
Externally publishedYes

Fingerprint

Online Optimization
Nonseparable
Decentralized
Averaging
Lipschitz
Convex optimization
Primal-dual Algorithm
Sensor networks
Regret
Convex Optimization
Undirected Graph
Digraph
Broadcast
Convex function
Sensor Networks
Horizon
Theoretical Analysis
Time-varying
Continuous Function
Complement

Keywords

  • Distributed convex optimization
  • dual averaging
  • multiagent systems
  • online optimization

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Control and Optimization

Cite this

Coordinate Dual Averaging for Decentralized Online Optimization with Nonseparable Global Objectives. / Lee, Soomin; Nedich, Angelia; Raginsky, Maxim.

In: IEEE Transactions on Control of Network Systems, Vol. 5, No. 1, 01.03.2018, p. 34-44.

Research output: Contribution to journalArticle

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