Generative Distributionally Robust Optimization

Generative models increasingly supply scenarios for downstream optimization, but the resulting decisions are vulnerable to model misspecification. Standard transport-based distributionally robust optimization (DRO) accepts arbitrary nominal samplers without requiring worst-case laws to respect generator structure, while existing generative ambiguity-set methods enforce such structure but typically rely on model-specific access or training-data certificates. We introduce Generative Distributionally Robust Optimization (GDRO), a general framework that accepts any pretrained conditional generative model as its nominal model and optimizes against adversarial laws induced by a chosen conditional generator family. The key is to pair sampler representations of conditional laws with a Sinkhorn certificate that compares nominal and adversarial output laws from samples alone. This enables generator-constrained robust optimization across explicit and implicit nominal models, controlling distributional proximity at the decision context without requiring nominal likelihoods or gradients. We develop a stochastic primal–dual algorithm for an expected mini-batch formulation and establish bounds linking Sinkhorn proximity to changes in expected downstream loss and quantifying the Lagrangian relaxation gap. Experiments span convex contextual newsvendor problems with explicit generators on synthetic and M5 retail demand data, and nonconvex robot navigation with the implicit SocialGAN generator. Relative to nominal decisions, GDRO reduces rare-context inventory regret by 63% on synthetic data and navigation collisions by 66%, while maintaining a 99.7% arrival rate.