We generalize the problem of online submodular welfare maximization to incorporate a variety of new elements arising from reusability, stochastic rewards, combinatorial actions and similar features that have received significant attention in recent years. For our general formulation, we show that a non-adaptive Greedy algorithm achieves the highest possible competitive ratio against an adaptive offline benchmark in the adversarial arrival model and in the unknown IID stochastic arrival model. In addition to generalizing several previous results, this shows that, in general, adaptivity to stochastic rewards (and similar features) offers no theoretical (worst-case) benefits.

翻译：我们推广了在线子模福利最大化问题，纳入了近年来备受关注的多种新要素，包括可复用性、随机奖励、组合动作等特性。针对这一通用形式，我们证明在对抗性到达模型和未知独立同分布随机到达模型中，非自适应贪婪算法相对于自适应离线基准能达到最高可能的竞争比。这一结果不仅推广了若干已有结论，还表明在一般情况下，适应随机奖励（及类似特性）在理论上（最坏情况下）并不带来收益。