Distributionally robust optimization adapts to better handle prediction errors
Calibrating Ambiguity Set via Diagnostic Transport for Distributionally Robust Optimization
Machine Learning
Summary
Decisions based on predictions can be too cautious when the uncertainty around those predictions is not represented well. The authors introduce a method called diagnostic-transport DRO (DT-DRO) that uses extra data to better understand and fix how uncertainty is measured. This approach adjusts the shape and size of uncertainty to match observed errors, leading to decisions that are less overly cautious. They prove their method can improve guarantees about decision risk and show it works better in tests, especially when the model assumptions are wrong.
What this means in practice
- •For supply chain planners: Create more accurate robust plans that avoid needless conservatism when facing uncertain demand forecasts with structural errors.
- •For energy grid operators: Improve outage response decisions by better capturing uncertainty in power availability predictions, especially under rare event conditions.
Authors
Wenbin Zhou, Elizabeth Cucuzzella, Shixiang Zhu
Abstract
Distributionally robust optimization (DRO) protects decisions against distributional uncertainty by optimizing over an ambiguity set, but poorly aligned set geometry can require large radii and yield overly conservative decisions. We introduce diagnostic-transport DRO (DT-DRO), which uses held-out calibration data to adapt the ambiguity-set geometry to observed predictive errors. DT-DRO uses the conditional probability integral transform cumulative distribution function to diagnose systematic probability misallocation and translates this information into an outcome-level transport that jointly adjusts the ambiguity-set center and ground cost. The resulting formulation admits a computationally tractable dual reformulation. Theoretically, we derive valid ambiguity radii and decision-risk guarantees that tighten as estimation and approximation errors vanish, and show that DT-DRO can eliminate the nonvanishing robustness floor caused by model misspecification. Synthetic experiments and a power-outage application demonstrate improved decision quality, particularly under structural and tail misspecification.