Online Submodular Welfare Maximization Meets Post-Allocation Stochasticity and Reusability

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.