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Distributionally robust optimization

Part of: Operations research, mathematical programming

Published online by Cambridge University Press:  01 July 2025

Daniel Kuhn Open the ORCID record for Daniel Kuhn [Opens in a new window] ,
Soroosh Shafiee  and
Wolfram Wiesemann
Daniel Kuhn
Affiliation:
Risk Analytics and Optimization Chair, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland E-mail: daniel.kuhn@epfl.ch
Soroosh Shafiee
Affiliation:
School of Operations Research and Information Engineering, Cornell University, Ithaca, NY, USA E-mail: shafiee@cornell.edu
Wolfram Wiesemann
Affiliation:
Imperial College Business School, Imperial College London, London SW7 2AZ, UK E-mail: ww@imperial.ac.uk
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Abstract

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Distributionally robust optimization (DRO) studies decision problems under uncertainty where the probability distribution governing the uncertain problem parameters is itself uncertain. A key component of any DRO model is its ambiguity set, that is, a family of probability distributions consistent with any available structural or statistical information. DRO seeks decisions that perform best under the worst distribution in the ambiguity set. This worst case criterion is supported by findings in psychology and neuroscience, which indicate that many decision-makers have a low tolerance for distributional ambiguity. DRO is rooted in statistics, operations research and control theory, and recent research has uncovered its deep connections to regularization techniques and adversarial training in machine learning. This survey presents the key findings of the field in a unified and self-contained manner.

MSC classification

Primary: 90-02: Research exposition (monographs, survey articles)
Secondary: 90C15: Stochastic programming 90C47: Minimax problems

Information

Type
Research Article
Information
Acta Numerica , Volume 34 , July 2025 , pp. 579 - 804
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2025. Published by Cambridge University Press

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