The Bayesian Prophet: A Low-Regret Framework for Online Decision Making
25 Pages Posted: 25 Apr 2018
Date Written: April 6, 2018
We consider a new framework for online policies for packing problems with stochastic arrivals, where the policy has access to an oracle that provides statistical information regarding the offline optimal solution; this forms an attempt to understand the increasing success of black-box predictive algorithms as subroutines for such problems.To this end, we first propose the Bayes Selector, a simple greedy policy for general online decision-making problems based on such an oracle, and provide a generic way to derive bounds on the expected regret (i.e., additive loss vis-a-vis the offline solution). We then prove that in any online packing problem with a discrete distribution over arrivals, the Bayes Selector achieves an expected regret which is independent of the number of arrivals and the starting resource levels. Our results are obtained via a novel coupling argument, as well as a new thresholding policy based on a dynamic LP relaxation; these techniques may be of independent interest for deriving oracle-driven policies for other online decision-making settings.
Keywords: Online Stochastic Optimization, Prophet Inequalities, Approximate Dynamic Programming, Network Revenue Management, Online Packing
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