Adaptive scenario selection improves robust decision making under uncertainty
Adaptive Scenario Generation for KL-DRO Around a Learned Density Model
Machine Learning
Summary
When making decisions based on limited data, it's important to prepare for possible rare events not seen before. The authors propose using a learned model to guess which new situations might be risky and focusing on those when planning. They build their scenarios step-by-step by picking new examples where decisions could go wrong, then adjust their plans accordingly. This method helps make better choices when data is scarce and conditions change in predictable ways, tested on problems like inventory and power grid planning.
What this means in practice
- •For supply chain planners: Improve inventory decisions by focusing on rare demand scenarios that a learned model predicts as costly but weren't seen in historical data.
- •For energy grid operators: Enhance capacity expansion plans by adapting scenario sets to emphasize difficult-to-predict demand or supply conditions modeled beyond past data.
Authors
Aron Brenner, Saurabh Amin
Abstract
Distributionally robust optimization (DRO) hedges data-driven two-stage stochastic programs against error in the distribution estimated from a finite record, and standard ambiguity sets differ in how they treat realizations absent from that record. A divergence ball around the empirical distribution contains only reweightings of the record, whereas a transport ball also contains distributions supported off the record, including on realizations the data-generating process cannot produce, against which the decision is then hedged as well. We instead propose a Kullback-Leibler (KL) ball centered at a density model fitted to the record, the learned nominal, which lets the adversary up-weight costly unobserved realizations in proportion to the probability the model assigns them. Solving the resulting problem poses a second difficulty, because it can accommodate only a few scenarios, and an independent sample of that size is likely to omit the rare realizations on which the worst case concentrates. We therefore build the scenario set adaptively, alternating between solving the finite problem and drawing new realizations from the learned nominal, steered toward the worst case at the current decision, with importance weights that correct the draws back to the model. On a multi-item newsvendor problem and a capacity expansion problem on realistic grid data, centering the ball at the learned nominal rather than at the record lowers cost under distribution shift, at comparable in-distribution cost, when the record is scarce and the model class captures structure that lets it extrapolate beyond the record. The advantage fades as the record grows or as the shift departs from the structure the model has learned.