The Benefits of Delay to Online Decision Making.

This article focuses on the theoretical and empirical analysis of the benefits of delaying real-time decisions in online resource allocation problems. It introduces the "delayed Bayesian prophet" algorithm, proving that its regret—measured as the performance gap compared to an offline optimal policy—decays exponentially with the length of the allowable delay. The study covers a broad class of problems, including the multisecretary problem, general online allocation with multiple resources, and applications in online order fulfillment, extending results to settings with independent but nonidentical arrivals, unknown arrival distributions, and batched decision-making. Numerical experiments using synthetic data and real-world data from JD.com demonstrate that even a small delay significantly reduces regret, while batching decisions offers smaller but still positive benefits. Overall, the findings suggest that modest delays in decision-making can substantially improve online allocation performance without incurring regret growth over time.