The Bayesian Prophet: A Low-Regret Framework for Online Decision Making
Motivated by the success of using black-box predictive algorithms as subroutines for online decision-making, 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 tackling 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 the Bayes Selector has constant expected regret (i.e., independent of the number of arrivals and resource levels) in any online packing and matching problem with a finite type-space. Our results generalize and simplify many existing results for online packing and matching problems, and suggest a promising pathway for obtaining oracle-driven policies for other online decision-making settings.