Communication-Efficient Decentralized Online Continuous DR-Submodular Maximization

Maximizing a monotone submodular function is a fundamental task in data mining, machine learning, economics, and statistics. In this paper, we present two communication-efficient decentralized online algorithms for the monotone continuous DR-submodular maximization problem, both of which reduce the number of perfunction gradient evaluations and per-round communication complexity from T-3/2 to 1. The first one, One-shot Decentralized MetaFrank-Wolfe (Mono-DMFW), achieves a ( 1 - 1/e)-regret bound of O(T-4/5). As far as we know, this is the first one-shot and projectionfree decentralized online algorithm for monotone continuous DRsubmodular maximization. Next, inspired by the non-oblivious boosting function [29], we propose the Decentralized Online Boosting Gradient Ascent (DOBGA) algorithm, which attains a (1- 1/e)-regret of O (root T). To the best of our knowledge, this is the first result to obtain the optimal O (root T) against a ( 1- 1/e)-approximation with only one gradient inquiry for each local objective function per step. Finally, various experimental results confirm the effectiveness of the proposed methods.