We investigate the online bandit learning of the monotone multi-linear DR-submodular functions, designing the algorithm \\(BanditMLSM\\) that attains \\(O(T^{2\/3}\\log T)\\) of \\((1\u22121\/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\u22121\/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})\\)\u00a0 \\((1\u22121\/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).<\/p>\n","protected":false},"excerpt":{"rendered":"
We investigate the online bandit learning of the monotone multi-linear DR-submodular functions, designing the algorithm that attains of -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 of -regret in both problems, which improve the existing results. 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