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

Junlong Zhu, Qingtao Wu, Mingchuan Zhang, Ruijuan Zheng, Keqin Li; 22(51):1−42, 2021.

### 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 $O(\sqrt{T})$ 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.

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