From Data to Decisions: Distributionally Robust Optimization Is Optimal

Van Parys, Bart P. G.; Esfahani, Peyman Mohajerin; Kuhn, Daniel

doi:10.1287/mnsc.2020.3678

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Journal article

From Data to Decisions: Distributionally Robust Optimization Is Optimal

Van Parys, Bart P. G. ORCID Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139;
Esfahani, Peyman Mohajerin ORCID Delft Center for Systems and Control, Technische Universiteit Delft, 2628 CD Delft, Netherlands;
Kuhn, Daniel ORCID Risk Analytics and Optimization Chair, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland

2020-11-23

Published in:

Management Science. - Institute for Operations Research and the Management Sciences (INFORMS). - 2020

Management Science and Operations Research

Strategy and Management

English 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.

Language

English

Open access status

green

Identifiers

DOI 10.1287/mnsc.2020.3678
ISSN 0025-1909

Persistent URL

https://sonar.ch/global/documents/256231

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