Optimal Model Selection for Conformalized Robust Optimization

While recent advances use conformal prediction to construct prediction sets for machine learning models, the downstream decisions critically depend on model selection. This paper introduces novel model selection frameworks for CRO that unify robustness control with decision risk minimization.

We first propose <i>Conformalized Robust Optimization with Model Selection</i> (CROMS), a framework that selects the model to approximately minimize the averaged decision risk in CRO solutions. Given the target robustness level 1−α, we present a computationally efficient algorithm called E-CROMS, which achieves asymptotic robustness control and decision optimality. To correct the control bias in finite samples, we further develop two algorithms: F-CROMS, which ensures a 1−α robustness but requires searching the label space; and J-CROMS, which offers lower computational cost while achieving a 1−2α robustness.