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：本文提出了一种统一的连续DR-子模函数最大化方法，该方法涵盖了多种设定和预言机访问类型。我们的方法包含一种针对单调和非单调函数的Frank-Wolfe型离线算法，并对一般凸集施加了不同限制。我们考虑了预言机提供函数梯度或仅提供函数值的设定，以及预言机访问是确定性的或随机性两种情况。我们在所有情形下确定了所需的预言机访问次数。在十六种考虑的情形中，我们的方法在九种情形下给出了新的/改进的结果，在两种情形下避免了计算成本高的投影操作，而在其余五种情形中，所提框架的性能与现有最优方法持平。值得注意的是，我们基于随机函数值预言机的方法首次为随机DR-子模函数赋予了带强盗反馈的遗憾界。