Bandit Multi-linear DR-Submodular Maximization and Its Applications on Adversarial Submodular Bandits

05/21/2023

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by   Zongqi Wan, et al.

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We investigate the online bandit learning of the monotone multi-linear DR-submodular functions, designing the algorithm 𝙱𝚊𝚗𝚍𝚒𝚝𝙼𝙻𝚂𝙼 that attains O(T^2/3log T) of (1-1/e)-regret. Then we reduce submodular bandit with partition matroid constraint and bandit sequential monotone maximization to the online bandit learning of the monotone multi-linear DR-submodular functions, attaining O(T^2/3log T) of (1-1/e)-regret in both problems, which improve the existing results. To the best of our knowledge, we are the first to give a sublinear regret algorithm for the submodular bandit with partition matroid constraint. A special case of this problem is studied by Streeter et al.(2009). They prove a O(T^4/5) (1-1/e)-regret upper bound. For the bandit sequential submodular maximization, the existing work proves an O(T^2/3) regret with a suboptimal 1/2 approximation ratio (Niazadeh et al. 2021).