KL-DRO centered on a learned density uses adaptive scenarios

On scarce records, a learned nominal lowered cost under distribution shift on newsvendor and grid capacity problems.

The paper centers a Kullback-Leibler ambiguity set on a density model fitted to a finite record, so an adversary can up-weight unobserved but plausible costly outcomes. Because only a few scenarios fit the solver, the authors build the set adaptively by alternating optimization with draws from the learned nominal steered toward the current worst case and corrected by importance weights. On a multi-item newsvendor and a capacity-expansion problem with realistic grid data, this lowered cost under distribution shift versus a ball around the empirical record when data were scarce, at similar in-distribution cost. The gain fades as the record grows or the shift leaves the model's learned structure.