Projection-free Decentralized Online Learning for Submodular Maximization over Time-Varying Networks

This paper considers a decentralized online submodular maximization problem over time-varying networks, where each agent only utilizes its own information and the received information from its neighbors. To address the problem, we propose a decentralized Meta-Frank-Wolfe online learning method in the adversarial online setting by using local communication and local computation. Moreover, we show that an expected regret bound of O(root T) is achieved with (1-1/e) approximation guarantee, where T is a time horizon. In addition, we also propose a decentralized one-shot Frank-Wolfe online learning method in the stochastic online setting. Furthermore, we also show that an expected regret bound O(T-2/3) is obtained with (1 - 1/e) approximation guarantee. Finally, we confirm the theoretical results via various experiments on different datasets.