Conformal-DRO: Distributionally Robust Optimization with Conformalized Ambiguity Set

2026-09-10

AI Summary

该论文提出了一种名为Conformal-DRO的方法，通过构建基于共形区域的模糊集来解决潜在分布异质性下的数据驱动分布鲁棒优化问题。

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.

Problem

• Distributionally Robust Optimization
• Latent Distributional Heterogeneity
• Ambiguity Set

Innovation

• Conformal-DRO
• Ambiguity Set
• Data-driven Transport Geometry
• Latent Distributional Heterogeneity
• Finite Linear Program