The Bayesian Prophet: A Low-Regret Framework for Online Decision Making

Extended abstract appeared in SIGMETRICS 2019

Forthcoming, Management Science

41 Pages Posted: 25 Apr 2018 Last revised: 27 Feb 2020

See all articles by Alberto Vera

Alberto Vera

Cornell University - School of Operations Research and Industrial Engineering

Siddhartha Banerjee

Cornell University - School of Operations Research and Information Engineering

Date Written: April 6, 2018

Abstract

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.

Keywords: Online Stochastic Optimization, Prophet Inequalities, Approximate Dynamic Programming, Network Revenue Management, Online Packing

Suggested Citation

Vera, Alberto and Banerjee, Siddhartha, The Bayesian Prophet: A Low-Regret Framework for Online Decision Making (April 6, 2018). Extended abstract appeared in SIGMETRICS 2019, Forthcoming, Management Science, Available at SSRN: https://ssrn.com/abstract=3158062 or http://dx.doi.org/10.2139/ssrn.3158062

Alberto Vera

Cornell University - School of Operations Research and Industrial Engineering ( email )

Ithaca, NY 14853
United States

Siddhartha Banerjee (Contact Author)

Cornell University - School of Operations Research and Information Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States

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