Robust Decisions via Generative Wasserstein Distributionally Robust Optimization

Decision-making under uncertainty is fundamental to many real-world applications, from energy systems to finance, where agents must make optimal decisions without knowing future outcomes. This work proposes Gen-WDRO, a novel generative Wasserstein distributionally robust optimization framework that combines conditional normalizing flows with distributionally robust optimization for robust decision-making under distribution shift. Our approach learns conditional distributions via normalizing flows, constructs Wasserstein ambiguity sets around these learned distributions, and employs neural networks to adaptively determine robustness radii. We prove that under linear cost structures, the resulting distributionally robust problem can be reformulated as a tractable convex optimization problem, enabling efficient end-to-end training that simultaneously improves performance and enhances robustness against distribution shift. Experiments on battery storage management under distribution shift demonstrate that Gen-WDRO achieves superior robustness with the best CVaR performance, validating the effectiveness of adaptive uncertainty quantification for robust decision-making.