Online Continuous Submodular Maximization: From Full-Information to Bandit Feedback

Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)

AuthorFeedback Bibtex MetaReview Metadata Paper Reviews Supplemental


Mingrui Zhang, Lin Chen, Hamed Hassani, Amin Karbasi


In this paper, we propose three online algorithms for submodular maximization. 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.