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

• URL: http://arxiv.org/abs/2305.12402v1
• Date: Sun, 21 May 2023 08:51:55 GMT
• Title: Bandit Multi-linear DR-Submodular Maximization and Its Applications on Adversarial Submodular Bandits
• Authors: Zongqi Wan, Jialin Zhang, Wei Chen, Xiaoming Sun, Zhijie Zhang
• Abstract summary: We give a sublinear regret algorithm for the submodular bandit with partition matroid constraint. For the bandit sequential submodular, the existing work proves an $O(T2/3)$ regret with a suboptimal $1/2$ approximation ratio.
• Score: 21.54858035450694
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the online bandit learning of the monotone multi-linear DR-submodular functions, designing the algorithm $\mathtt{BanditMLSM}$ that attains $O(T^{2/3}\log T)$ 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 $O(T^{2/3}\log T)$ 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).

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