Online Continuous Submodular Maximization: From Full-Information to Bandit Feedback
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Abstract
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 
[18] and 
[17] to 1, and achieves a 
-regret bound of 
The second one, Bandit-Frank-Wolfe, is the first bandit algorithm for continuous DR-submodular maximization, which achieves a 
-regret bound of 
. Finally, we extend Bandit-Frank-Wolfe to a bandit algorithm for discrete submodular maximization, Responsive-Frank-Wolfe, which attains a -regret bound of 
in the responsive bandit setting.
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