Recovering Best Statistical Guarantees via the Empirical Divergence-Based Distributionally Robust Optimization

Abstract

AboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareShare onFacebookTwitterLinked InEmail Go to Section HomeOperations ResearchVol. 67, No. 4 Recovering Best Statistical Guarantees via the Empirical Divergence-Based Distributionally Robust OptimizationHenry Lam Henry Lam Published Online:2 Jul 2019https://doi.org/10.1287/opre.2018.1786AbstractWe investigate the use of distributionally robust optimization (DRO) as a tractable tool to recover the asymptotic statistical guarantees provided by the central limit theorem, for maintaining the feasibility of an expected value constraint under ambiguous probability distributions. We show that using empirically defined Burg-entropy divergence balls to construct the DRO can attain such guarantees. These balls, however, are not reasoned from the standard data-driven DRO framework because, by themselves, they can have low or even zero probability of covering the true distribution. Rather, their superior statistical performances are endowed by linking the resulting DRO with empirical likelihood and empirical processes. We show that the sizes of these balls can be optimally calibrated using χ2-process excursion. We conduct numerical experiments to support our theoretical findings. Previous Back to Top Next FiguresReferencesRelatedInformationCited byA chance constraint microgrid energy management with phase balancing using electric vehicle demand aggregation12 January 2023 | Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, Vol. 45, No. 1The Value of Randomized Strategies in Distributionally Robust Risk-Averse Network Interdiction ProblemsUtsav Sadana, Erick Delage6 December 2022 | INFORMS Journal on Computing, Vol. 35, No. 1Distributionally Robust Optimization for Input Model Uncertainty in Simulation-Based Decision MakingData-Driven Chance Constrained Programs over Wasserstein BallsZhi Chen, Daniel Kuhn, Wolfram Wiesemann21 July 2022 | Operations Research, Vol. 0, No. 0Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of DimensionalityRui Gao20 July 2022 | Operations Research, Vol. 0, No. 0Robust Simulation with Likelihood-Ratio Constrained Input UncertaintyZhaolin Hu, L. Jeff Hong25 March 2022 | INFORMS Journal on Computing, Vol. 34, No. 4Distributionally Robust Optimization with Confidence Bands for Probability Density FunctionsXi Chen, Qihang Lin, Guanglin Xu6 October 2021 | INFORMS Journal on Optimization, Vol. 4, No. 1Data-Driven Robust Resource Allocation with Monotonic Cost FunctionsYe Chen, Nikola Marković, Ilya O. Ryzhov, Paul Schonfeld1 December 2021 | Operations Research, Vol. 70, No. 1Input Uncertainty in Stochastic Simulation8 July 2022On Solving Distributionally Robust Optimization Formulations EfficientlyTwo-Time-Scale Energy Management for Microgrids With Data-Based Day-Ahead Distributionally Robust Chance-Constrained SchedulingIEEE Transactions on Smart Grid, Vol. 12, No. 6Statistical Analysis of Wasserstein Distributionally Robust EstimatorsJose Blanchet, Karthyek Murthy, Viet Anh Nguyen18 October 2021Learning-Based Robust Optimization: Procedures and Statistical GuaranteesL. Jeff Hong, Zhiyuan Huang, Henry Lam22 December 2020 | Management Science, Vol. 67, No. 6A data-driven approach to beating SAA out-of-sampleSSRN Electronic Journal, Vol. 25Parametric Scenario Optimization under Limited Data25 November 2020 | ACM Transactions on Modeling and Computer Simulation, Vol. 30, No. 4Scenario-Wise Distributionally Robust Optimization for Collaborative Intermittent Resources and Electric Vehicle Aggregator Bidding StrategyIEEE Transactions on Power Systems, Vol. 35, No. 5Validating Optimization with Uncertain ConstraintsOptimization-Based Calibration of Simulation Input ModelsAleksandrina Goeva, Henry Lam, Huajie Qian, Bo Zhang1 August 2019 | Operations Research, Vol. 67, No. 5 Volume 67, Issue 4July-August 2019Pages ii-iv, 905-1208 Article Information Supplemental Materials Metrics Information Received:May 30, 2016Accepted:May 10, 2018Published Online:July 02, 2019 Copyright © 2019, INFORMSCite asHenry Lam (2019) Recovering Best Statistical Guarantees via the Empirical Divergence-Based Distributionally Robust Optimization. Operations Research 67(4):1090-1105. https://doi.org/10.1287/opre.2018.1786 Keywordsdistributionally robust optimizationempirical likelihoodempirical processchi-square processcentral limit theoremPDF download