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.

翻译：本文提出了一种用于最大化连续DR-子模函数的统一方法，该方法涵盖了多种设置和预言机访问类型。我们的方法包括一种针对单调函数和非单调函数的Frank-Wolfe类离线算法，并对一般凸集施加了不同的限制条件。我们考虑了以下场景：预言机提供对函数梯度的访问或仅提供函数值的访问，且预言机访问是确定性的或随机性的。我们在所有情况下确定了所需的预言机访问次数。我们的方法在十六种考虑的情况中为九种提供了新的/改进的结果，避免了两种情况下计算代价高昂的投影，并在其余五种情况下，所提出的框架与现有最优方法性能相匹配。值得注意的是，针对随机函数值型预言机，我们的方法首次实现了随机DR-子模函数在基于强盗反馈下的遗憾界。