This paper introduces unified projection-free Frank-Wolfe type algorithms for adversarial continuous DR-submodular optimization, spanning scenarios such as full information and (semi-)bandit feedback, monotone and non-monotone functions, different constraints, and types of stochastic queries. For every problem considered in the non-monotone setting, the proposed algorithms are either the first with proven sub-linear $\alpha$-regret bounds or have better $\alpha$-regret bounds than the state of the art, where $\alpha$ is a corresponding approximation bound in the offline setting. In the monotone setting, the proposed approach gives state-of-the-art sub-linear $\alpha$-regret bounds among projection-free algorithms in 7 of the 8 considered cases while matching the result of the remaining case. Additionally, this paper addresses semi-bandit and bandit feedback for adversarial DR-submodular optimization, advancing the understanding of this optimization area.

翻译：本文提出用于对抗性连续DR-子模优化的统一无投影Frank-Wolfe型算法，涵盖全信息与（半）赌博机反馈、单调与非单调函数、不同约束条件以及随机查询类型等多种场景。针对非单调设置下考虑的每个问题，所提出的算法要么是首个具有可证明亚线性α-遗憾界的方案，要么相比现有技术具有更优的α-遗憾界，其中α为离线场景中对应的近似界。在单调设置中，所提方法在8个案例中的7个实现了无投影算法中领先的亚线性α-遗憾界，并达到了剩余案例的同等性能。此外，本文还探讨了面向对抗性DR-子模优化的半赌博机与赌博机反馈，推进了对这一优化领域的理解。