Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach

John C. Duchi (), Peter W. Glynn () and Hongseok Namkoong ()
Additional contact information
John C. Duchi: Department of Electrical Engineering and Statistics, Stanford University, Stanford, California 94305
Peter W. Glynn: Department of Management Science and Engineering, Stanford University, Stanford, California 94305
Hongseok Namkoong: Decision, Risk, and Operations Division, Columbia Business School, New York City, NY 10027

Mathematics of Operations Research, 2021, vol. 46, issue 3, 946-969

Abstract: We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a generalized empirical likelihood framework—based on distributional uncertainty sets constructed from nonparametric f -divergence balls—for Hadamard differentiable functionals, and in particular, stochastic optimization problems. As consequences of this theory, we provide a principled method for choosing the size of distributional uncertainty regions to provide one- and two-sided confidence intervals that achieve exact coverage. We also give an asymptotic expansion for our distributionally robust formulation, showing how robustification regularizes problems by their variance. Finally, we show that optimizers of the distributionally robust formulations we study enjoy (essentially) the same consistency properties as those in classical sample average approximations. Our general approach applies to quickly mixing stationary sequences, including geometrically ergodic Harris recurrent Markov chains.

Keywords: Primary: 62Mxx inference from stochastic processes; Primary: Programming/stochastic; secondary: statistics; stochastic optimization; robust optimization; empirical likelihood (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://dx.doi.org/10.1287/moor.2020.1085 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:46:y:2021:i:3:p:946-969

Access Statistics for this article

More articles in Mathematics of Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().