Optimal Model Selection for Conformalized Robust Optimization
This work addresses model selection for decision-making under uncertainty, advancing conformal prediction methodology with covariate-aware selection, though it is incremental in building on existing robust optimization and conformal prediction methods.
The paper tackles the problem of model selection in contextual robust optimization by introducing frameworks that unify robustness control with decision risk minimization, resulting in significant improvements in decision efficiency and robustness across synthetic and real-world applications.
In decision-making under uncertainty, Contextual Robust Optimization (CRO) provides reliability by minimizing the worst-case decision loss over a prediction set, hedging against label variability. 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 Conformalized Robust Optimization with Model Selection (CROMS), which automatically selects models to approximately minimize the average decision risk in CRO solutions. We develop two algorithms: E-CROMS, which is computationally efficient, and F-CROMS, which enjoys a marginal robustness guarantee in finite samples. Further, we introduce Conformalized Robust Optimization with Individualized Model Selection (CROiMS), which performs individualized model selection by minimizing the conditional decision risk given the covariate of test data. This framework advances conformal prediction methodology by enabling covariate-aware model selection. Theoretically, CROiMS achieves asymptotic conditional robustness and decision efficiency under mild assumptions. Numerical results demonstrate significant improvements in decision efficiency and robustness across diverse synthetic and real-world applications, outperforming baseline approaches.