Conformal Contextual Robust Optimization

Predict-then-optimize or contextual robust optimization problems are of long-standing interest in safety-critical settings where decision-making happens under uncertainty (Sun, Liu, and Li, 2023; Elmachtoub and Grigas, 2022; Elmachtoub, Liang, and McNellis, 2020; Peršak and Anjos, 2023). In traditional robust optimization, results are made to be robust to distributions anticipated to be present upon deployment (Ben-Tal, El Ghaoui, and Nemirovski, 2009; Beyer and Sendhoff, 2007). Since such decisions are sensitive to proper model specification, recent efforts have sought to supplant this with data-driven uncertainty regions (Cheramin et al., 2021; Bertsimas, Gupta, and Kallus, 2018; Shang and You, 2019; Johnstone and Cox, 2021). Model misspecification is ever more present in contextual robust optimization, spurring efforts to define similar datadriven uncertainty regions (Ohmori, 2021; Chenreddy, Bandi, and Delage, 2022; Sun, Liu, and Li, 2023). Such methods, however, focus on box-and ellipsoid-based uncertainty regions, both of which are necessarily convex and often overly conservative, resulting in suboptimal decision-making. Conformal prediction provides a principled framework for producing distribution-free prediction regions with marginal frequentist coverage guarantees (Angelopoulos and Bates, 2021; Shafer and Vovk, 2008).