Mean robust optimization
Name
10107_2024_2170_ReferencePDF.pdf
Size
1.29 MB
Format
Adobe PDF
Checksum (MD5)
12414bc19009ed67ec8c0ba8fd64fa5f
Author(s)
Wang, Irina
Becker, Cole
Van Parys, Bart
Stellato, Bartolomeo
Date Issued
November 28, 2024
Journal
Mathematical Programming
Publisher
Springer Berlin Heidelberg
Citation
Wang, I., Becker, C., Van Parys, B. et al. Mean robust optimization. Math. Program. 213, 1235–1277 (2025).
Version
Author's final manuscript
Abstract
Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein distributionally robust optimization can reduce conservatism by being data-driven, but it often leads to very large problems with prohibitive solution times. We introduce mean robust optimization, a general framework that combines the best of both worlds by providing a trade-off between computational effort and conservatism. We propose uncertainty sets constructed based on clustered data rather than on observed data points directly thereby significantly reducing problem size. By varying the number of clusters, our method bridges between robust and Wasserstein distributionally robust optimization. We show finite-sample performance guarantees and explicitly control the potential additional pessimism introduced by any clustering procedure. In addition, we prove conditions for which, when the uncertainty enters linearly in the constraints, clustering does not affect the optimal solution. We illustrate the efficiency and performance preservation of our method on several numerical examples, obtaining multiple orders of magnitude speedups in solution time with little-to-no effect on the solution quality.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10107-024-02170-4
