Calibrating Ambiguity Set via Diagnostic Transport for Distributionally Robust Optimization
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.
Related
- Conformal-DRO: Distributionally Robust Optimization with Conformalized Ambiguity Set
- Local-discrepancy ambiguity sets for distributionally robust optimization
- Distributionally robust chance-constrained standard quadratic optimization with Wasserstein ambiguity
- A Composite Bayesian Risk--Distributionally Robust Optimization Model for Stochastic Programming with Elliptical Distribution Ambiguity
- Distributionally robust decision-making under ambiguity: case study of water environmental management
BibTeX
@misc{zhou2026calibrating,
title = {{Calibrating Ambiguity Set via Diagnostic Transport for Distributionally Robust Optimization}},
author = {Wenbin Zhou and Elizabeth Cucuzzella and Shixiang Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10793},
eprint = {2610.10793},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10793},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Calibrating Ambiguity Set via Diagnostic Transport for Distributionally Robust Optimization
AU - Wenbin Zhou
AU - Elizabeth Cucuzzella
AU - Shixiang Zhu
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10793
UR - https://arxiv.org/abs/2610.10793
AB - 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.
ER -