Worst-case generation via minimax optimization in Wasserstein space

In many high-stakes engineering and operational systems, such as autonomous vehicles [71], power systems [55], and healthcare [24], the outcomes that are most consequential for reliability, risk management, and decision-making arise not from typical observations, but from low-probability, high-impact scenarios situated at the periphery of the data-generating distribution. Such scenarios--stemming from atypical environmental conditions, irregular system configurations, or broader distributional shifts--often exert disproportionate influence on system performance. Yet, they are intrinsically difficult to observe, anticipate, or replicate through standard data-driven methods. Consequently, the ability to systematically construct informative worst-case samples is essential for rigorous stress testing, robustness certification, and the evaluation of models under meaningful but unobserved operating regimes. This need aligns with recent developments in generative modeling aimed at extreme-scenario synthesis, thereby enabling the identification of structural vulnerabilities that remain obscured under nominal data conditions. A natural framework for representing inference or decision-making systems under such worst-case scenarios is distributionally robust optimization (DRO), which minimizes expected loss over an ambiguity set of probability distributions and thereby provides a principled mechanism for modeling distributional uncertainty in stochastic optimization. Within this paradigm, Wasserstein DRO has emerged as a popular approach due to its geometry-aware ambiguity sets, which both capture realistic data perturbations and offer strong out-of-sample guarantees.