Online Continuous Submodular Maximization: From Full-Information to Bandit Feedback
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In this paper, we propose three online algorithms for submodular maximisation. The first one, Mono-Frank-Wolfe, reduces the number of per-function gradient evaluations from T^1/2 [Chen2018Online] and T^3/2 [chen2018projection] to 1, and achieves a (1-1/e)-regret bound of O(T^4/5). The second one, Bandit-Frank-Wolfe, is the first bandit algorithm for continuous DR-submodular maximization, which achieves a (1-1/e)-regret bound of O(T^8/9). Finally, we extend Bandit-Frank-Wolfe to a bandit algorithm for discrete submodular maximization, Responsive-Frank-Wolfe, which attains a (1-1/e)-regret bound of O(T^8/9) in the responsive bandit setting.
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