Coordinate Dual Averaging for Decentralized Online Optimization with Nonseparable Global Objectives

TL;DR

This paper introduces two decentralized algorithms, ODA-C and ODA-PS, for online convex optimization in networks, achieving sublinear regret bounds and validated through sensor network experiments.

Contribution

The paper develops two novel decentralized primal-dual algorithms with dual averaging for nonseparable global objectives in online optimization.

Findings

Both algorithms achieve O(√T) regret bounds.

Algorithms perform well on sensor network experiments.

Effective handling of nonseparable global objectives in decentralized settings.

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 over a static undirected graph. In ODA-PS, the agents implement the broadcast-based push-sum dynamics over a time-varying sequence of uniformly connected digraphs. We show that the regret bounds in both cases have sublinear growth of $O(\sqrt{T})$, with the time horizon $T$, when the stepsize is of the form $1/\sqrt{t}$ 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.