From Data to Decisions: Distributionally Robust Optimization Is Optimal
Name
1704.04118.pdf
Description
Submitted version
Size
573.71 KB
Format
Adobe PDF
Checksum (MD5)
b5d89be84fecf1394389a4ad0a870ca1
Author(s)
Van Parys, Bart PG
Esfahani, Peyman Mohajerin
Kuhn, Daniel
Date Issued
2021
Journal
Management Science
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Van Parys, Bart PG, Esfahani, Peyman Mohajerin and Kuhn, Daniel. 2021. "From Data to Decisions: Distributionally Robust Optimization Is Optimal." Management Science, 67 (6).
Version
Original manuscript
Abstract
We study stochastic programs where the decision maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution. In this setting, the goal is to find a procedure that transforms the data to an estimate of the expected cost function under the unknown data-generating distribution, that is, a predictor, and an optimizer of the estimated cost function that serves as a near-optimal candidate decision, that is, a prescriptor. As functions of the data, predictors and prescriptors constitute statistical estimators. We propose a meta-optimization problem to find the least conservative predictors and prescriptors subject to constraints on their out-of-sample disappointment. The out-of-sample disappointment quantifies the probability that the actual expected cost of the candidate decision under the unknown true distribution exceeds its predicted cost. Leveraging tools from large deviations theory, we prove that this meta-optimization problem admits a unique solution: The best predictor-prescriptor-pair is obtained by solving a distributionally robust optimization problem over all distributions within a given relative entropy distance from the empirical distribution of the data. This paper was accepted by Chung Piaw Teo, optimization.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1287/MNSC.2020.3678
