One-Point Residual Feedback Algorithms for Distributed Online Convex and Non-convex Optimization
Yaowen Wang, Lipo Mo, Min Zuo, Yuanshi Zheng
TL;DR
The paper tackles distributed online convex and non-convex optimization under non-stationary objective sequences. It extends the one-point residual feedback (ORF) gradient estimator to multi-agent networks with undirected, doubly-stochastic graphs, proposing two distributed algorithms that update each agent via a consensus-plus-gradient step using ORF estimates. The authors establish sublinear static regret guarantees that depend on local Lipschitz/smoothness and the cumulative variation of the objective, quantified by $\Theta_T$, for both convex and non-convex cases, and show improved (lower-variance) performance over conventional one-point methods. Numerical experiments on distributed convex optimization and resources allocation corroborate the theoretical results and demonstrate practical efficacy in scalable online learning over networks.
Abstract
This paper mainly addresses the distributed online optimization problem where the local objective functions are assumed to be convex or non-convex. First, the distributed algorithms are proposed for the convex and non-convex situations, where the one-point residual feedback technology is introduced to estimate gradient of local objective functions. Then the regret bounds of the proposed algorithms are derived respectively under the assumption that the local objective functions are Lipschitz or smooth, which implies that the regrets are sublinear. Finally, we give two numerical examples of distributed convex optimization and distributed resources allocation problem to illustrate the effectiveness of the proposed algorithm.