Print Email Facebook Twitter From data to decisions Title From data to decisions: Distributionally robust optimization is optimal Author van Parys, Bart P.G. (Massachusetts Institute of Technology) Mohajerin Esfahani, P. (TU Delft Team Peyman Mohajerin Esfahani) Kuhn, Daniel (Swiss Federal Institute of Technology) Date 2021 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. Subject Convex optimizationData-driven optimizationDistributionally robust optimizationLarge deviations theoryRelative entropy To reference this document use: http://resolver.tudelft.nl/uuid:211a0275-541b-4903-96d0-5dce278e056d DOI https://doi.org/10.1287/mnsc.2020.3678 Embargo date 2021-05-23 ISSN 0025-1909 Source Management Science, 67 (6), 3387-3402 Bibliographical note Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. Part of collection Institutional Repository Document type journal article Rights © 2021 Bart P.G. van Parys, P. Mohajerin Esfahani, Daniel Kuhn Files PDF mnsc.2020.3678.pdf 1.23 MB Close viewer /islandora/object/uuid:211a0275-541b-4903-96d0-5dce278e056d/datastream/OBJ/view