Communication-Efficient Decentralized Online Continuous DR-Submodular Maximization
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Maximizing a monotone submodular function is a fundamental task in 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 per-function gradient evaluations and per-round communication complexity from T^3/2 to 1. The first one, One-shot Decentralized Meta-Frank-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 projection-free decentralized online algorithm for monotone continuous DR-submodular maximization. Next, inspired by the non-oblivious boosting function <cit.>, we propose the Decentralized Online Boosting Gradient Ascent (DOBGA) algorithm, which attains a (1-1/e)-regret of O(√(T)). To the best of our knowledge, this is the first result to obtain the optimal O(√(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.
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