On the optimality of affine decision rules in robust and distributionally robust optimization
File(s)
Accepted version
Author(s)
Georghiou, Angelos
Tsoukalas, Angelos
Wiesemann, Wolfram
Type
Journal Article
Abstract
We propose conditions under which two-stage distributionally robust optimization problems are optimally solved in affine or K-adaptable affine decision rules. Contrary to previous work, our conditions do not impose any structure on the support of the uncertain parameters, and they ensure pointwise (as opposed to worst case) optimality of (K-adaptable) affine decision rules. The absence of support restrictions allows us to transfer nonlinearities from the problem description to the support via liftings, whereas the pointwise optimality implies that decision rules remain optimal for broad classes of distributionally robust optimization problems, including data-driven problems over 𝜙-divergence or Wasserstein ambiguity sets. We demonstrate how our conditions can be met in two applications.
Date Issued
2026-02-01
Date Acceptance
2025-04-07
Citation
Management science, 2026, 72 (2), pp.1456-1471
ISSN
0025-1909
Publisher
Institute for Operations Research and Management Sciences
Start Page
1456
End Page
1471
Journal / Book Title
Management science
Volume
72
Issue
2
Copyright Statement
Copyright © 2025, INFORMS. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Publication Status
Published
Date Publish Online
2025-06-11