# Conformal-DRO: Distributionally Robust Optimization with Conformalized Ambiguity Set

arXiv: https://arxiv.org/abs/2609.11073 · HTML: https://mlsanity.com/paper/2609.11073/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 24 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Distributionally Robust Optimization: A Review](https://mlsanity.com/paper/1908.05659/) (2019)
- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [Conformal e-prediction](https://mlsanity.com/paper/2001.05989/) (2020)
- [Distributionally robust stochastic programs with side information based on trimmings -- Extended version](https://mlsanity.com/paper/2009.10592/) (2020)
- [Distributionally Robust Weighted k-Nearest Neighbors](https://mlsanity.com/paper/2006.04004/) (2020)
- [Generative Conformal Prediction with Optimized Coverage Allocation](https://mlsanity.com/paper/2410.13735/) (2024)
- [Topology-Aware Conformal Prediction for Stream Networks](https://mlsanity.com/paper/2503.04981/) (2025)
- [Beyond Prediction: Conformal Inference for Latent Distributional Parameters](https://mlsanity.com/paper/2608.03607/) (2026)
- [Learning Polyhedral Conformal Sets for Robust Optimization](https://mlsanity.com/paper/2605.08506/) (2026)

## Built on by (most cited first, 1 of 1)

- [Calibrating Ambiguity Set via Diagnostic Transport for Distributionally Robust Optimization](https://mlsanity.com/paper/2610.10793/) (2026)

## Abstract (arXiv)

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.