Learning Context-Matched Uncertainty Representations for Robust Optimization

Two-stage robust optimization is shaped by the adversarial scenarios admitted by its uncertainty set. When side information is observed before a decision, learning this set from paired context–scenario data requires both identifying relevant historical uncertainty patterns and representing their nearby variation. However, a learned uncertainty set may still admit scenarios poorly matched to the observed context. The adversarial problem can return these scenarios when they maximize recourse cost. Existing methods restrict such scenarios through context-matching constraints in the adversarial problem, which can complicate its solution and require problem-specific reformulations. To address this issue, we propose CUB-RO, a nonparametric uncertainty-set learner that incorporates context matching into set construction, avoiding additional context-matching constraints in the adversarial problem. Given a new context, CUB-RO retrieves the K nearest historical contexts using a prespecified dissimilarity measure and constructs the uncertainty set as a union of local regions around their paired complete scenarios. The matched centers and local radii jointly determine the uncertainty-set boundary. We establish sufficient conditions for the learned set to converge to the true conditional support as the sample size grows. Moreover, we derive finite-sample bounds on the excess worst-case cost of the resulting decisions relative to the true conditional optimum. Experiments on Feature-Based Newsvendor (FBNV), Robust Portfolio Optimization (RPO), and Security-Constrained Unit Commitment (SCUC) show improvements over the evaluated baselines on the respective primary metrics. Compared with robust optimization using only the retrieved historical scenarios as the uncertainty set, CUB-RO reduces value-at-risk and conditional value-at-risk on RPO by 10.63% and 12.92%, respectively, and lowers mean realized costs by 4.78% on FBNV and 0.58% on SCUC.