From Data to Decisions: Distributionally Robust Optimization Is Optimal

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

Management Science, 2021, vol. 67, issue 6, 3387-3402

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.

Keywords: data-driven optimization; distributionally robust optimization; large deviations theory; relative entropy; convex optimization (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (15)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:67:y:2021:i:6:p:3387-3402

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