The Bayesian Prophet: A Low-Regret Framework for Online Decision Making
This provides a general framework for online decision-making with statistical predictions, potentially simplifying and extending results in areas like resource allocation and matching.
The paper tackles the problem of designing online policies with access to prediction oracles, and shows that a greedy policy called the Bayes Selector achieves constant expected regret for a class of online allocation problems, including Online Packing and Online Matching.
We develop a new framework for designing online policies given access to an oracle providing statistical information about an offline benchmark. Having access to such prediction oracles enables simple and natural Bayesian selection policies, and raises the question as to how these policies perform in different settings. Our work makes two important contributions towards this question: First, we develop a general technique we call *compensated coupling* which can be used to derive bounds on the expected regret (i.e., additive loss with respect to a benchmark) for any online policy and offline benchmark. Second, using this technique, we show that a natural greedy policy, which we call *the Bayes Selector*, has constant expected regret (i.e., independent of the number of arrivals and resource levels) for a large class of problems we refer to as Online Allocation with finite types, which includes widely-studied Online Packing and Online Matching problems. Our results generalize and simplify several existing results for Online Packing and Online Matching, and suggest a promising pathway for obtaining oracle-driven policies for other online decision-making settings.