We　investigate　the　online　bandit　learning　of　the　monotone　multi-linear　DR-submodular　functions,　designing　the　algorithm　BanditMLSM　that　attains　O(T2/3　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(T2/3　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(T4/5)　(1　−　1/e)-regret　upper　bound.　For　the　bandit　sequential　submodular　maximization,　the　existing　work　proves　an　O(T2/3)　regret　with　a　suboptimal　1/2　approximation　ratio　(Niazadeh　et　al.,　2021).　©　2023　Proceedings　of　Machine　Learning　Research.　All　rights　reserved.