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适用于单调和非单调函数的Frank-Wolfe型离线算法，并对一般凸集施加不同约束。我们考虑以下场景：预言机提供函数梯度或仅提供函数值访问，且预言机访问方式为确定性或随机性。我们确定了所有情况下所需的预言机访问次数。该方法在十六种考虑情况中的九种中给出了新的/改进的结果，在两种情况下避免了计算代价高昂的投影，其余五种情况下所提框架的性能与最优方法持平。值得注意的是，对于基于随机函数值的预言机，我们的方法首次实现了随机DR-子模函数在强盗反馈下的遗憾界。