Conformal-DRO: Distributionally Robust Optimization with Conformalized Ambiguity Set

Contextual stochastic optimization commonly assumes that instances with the same observed context share a single outcome distribution. We instead study latent conditional-law heterogeneity, where each instance has its own unobserved law but contributes only one outcome. We propose \texttt{Conformal-DRO}, a measure-inversion framework that converts split-conformal outcome coverage into an ambiguity set for the future latent law. Under exchangeability, this set contains the future law with a prescribed marginal finite-sample probability, without estimating historical latent laws or their mixing mechanism. For finitely supported aggregation rules, the resulting DRO problem reduces exactly to a linear program over conformal-shell masses, admits a scalar dual, and has a worst-case law supported on at most two shells. We further develop a sparse, decision-aware procedure for selecting conformal levels using independent tuning data. Synthetic experiments illustrate the learned ambiguity geometry and the effect of its resolution on the robust value.