Conformal-DRO: Distributionally Robust Optimization with Conformalized Ambiguity Set
Abstract
Data-driven distributionally robust optimization (DRO) typically treats the conditional outcome law as fixed and uses ambiguity sets to capture estimation error. This paper studies latent distributional heterogeneity, where each instance has an unobserved law but contributes only one observation, so uncertainty persists even if the mixture law is known. We propose Conformal-DRO, which uses nested conformal regions to construct an ambiguity set for the future latent law. Under exchangeability, the set covers this law with probability at least 1−α in finite samples, without estimating underlying latent laws or their mixing mechanism. The conformal path induces a data-driven transport geometry, while α determines the radius. The worst-case problem reduces to a finite linear program over conformal shells and admits sparse adversarial solutions. The resulting robust value provides a finite-sample certificate for the selected decision's expected cost.
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BibTeX
@misc{zhang2026conformaldro,
title = {{Conformal-DRO: Distributionally Robust Optimization with Conformalized Ambiguity Set}},
author = {Luhao Zhang and Shixiang Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11073},
eprint = {2609.11073},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11073},
}
RIS
TY - UNPB
TI - Conformal-DRO: Distributionally Robust Optimization with Conformalized Ambiguity Set
AU - Luhao Zhang
AU - Shixiang Zhu
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11073
UR - https://arxiv.org/abs/2609.11073
AB - Data-driven distributionally robust optimization (DRO) typically treats the conditional outcome law as fixed and uses ambiguity sets to capture estimation error. This paper studies latent distributional heterogeneity, where each instance has an unobserved law but contributes only one observation, so uncertainty persists even if the mixture law is known. We propose Conformal-DRO, which uses nested conformal regions to construct an ambiguity set for the future latent law. Under exchangeability, the set covers this law with probability at least 1−α in finite samples, without estimating underlying latent laws or their mixing mechanism. The conformal path induces a data-driven transport geometry, while α determines the radius. The worst-case problem reduces to a finite linear program over conformal shells and admits sparse adversarial solutions. The resulting robust value provides a finite-sample certificate for the selected decision's expected cost.
ER -