This paper presents a unified approach for maximizing continuous DR-submodular functions that encompasses a range of settings and oracle access types. Our approach includes a Frank-Wolfe type offline algorithm for both monotone and non-monotone functions, with different restrictions on the general convex set. We consider settings where the oracle provides access to either the gradient of the function or only the function value, and where the oracle access is either deterministic or stochastic. We determine the number of required oracle accesses in all cases. Our approach gives new/improved results for nine out of the sixteen considered cases, avoids computationally expensive projections in two cases, with the proposed framework matching performance of state-of-the-art approaches in the remaining five cases. Notably, our approach for the stochastic function value-based oracle enables the first regret bounds with bandit feedback for stochastic DR-submodular functions.

该论文提出了一种统一的方法来最大化连续DR-submodular函数，包括了一系列设置和oracle访问类型，并且给出了新的结果和改进的结果，其中包括一些与随机函数值有关的访问，使得其能够实现首个带有绑架反馈的悔恨边界。

最大化连续DR-次模函数的统一方法