Projection-free decentralized online learning for submodular maximization over time-varying networks

Zhu Junlong, Qingtao Wu, Mingchuan Zhang, Ruijuan Zheng, Keqin Li

Abstract: 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 $O(√T)$ is achieved with (1 &mdash $1/e$) 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 &mdash $1/e$) approximation guarantee. Finally, we confirm the theoretical results via various experiments on different datasets.