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 work 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. This work is available on https://arxiv.org/abs/2507.04716.

Haojie Ren is currently an Associate Professor in School of Mathematical Sciences, Shanghai Jiao Tong University. Prior to this, she was an Eberly Postdoc Fellow in the Department of Statistics, The Pennsylvania State University from 2019 to 2021.  She received her B.S, M.S, and Ph.D. in Statistics from Nankai University in 2013, 2016, 2018, respectively. Her research interest is on Predictive inference Change-point detection and outlier identification, and Massive data analysis. Haojie has published more than 20 papers on JASA, Biometrika and so on.