On the Optimality of Affine Decision Rules in Distributionally Robust Optimization
提出了两阶段分布鲁棒优化问题在仿射或K-自适应仿射决策规则下达到最优的条件，不依赖不确定参数支撑集的结构，并保证逐点最优性，适用于数据驱动问题。
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 [Formula: see text]-divergence or Wasserstein ambiguity sets. We demonstrate how our conditions can be met in two applications. This paper was accepted by Chung Piaw Teo, optimization and decision analytics. Funding: This work was supported by Engineering and Physical Sciences Research Council (EPSRC) [Grant EP/W003317/1]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2023.00053 .