In decision-making under uncertainty, Contextual Robust Optimization (CRO) provides reliability by minimizing the worst-case decision loss over a prediction set. 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), 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-αrobustness but requires searching the label space; and J-CROMS, which offers lower computational cost while achieving a 1-2αrobustness. Furthermore, we extend the CROMS framework to the individualized setting, where model selection is performed by minimizing the conditional decision risk given the covariates of the test data. This framework advances conformal prediction methodology by enabling covariate-aware model selection. Numerical results demonstrate significant improvements in decision efficiency across diverse synthetic and real-world applications, outperforming baseline approaches.

翻译：在不确定性下的决策过程中，上下文鲁棒优化通过最小化预测集上的最坏情况决策损失来提供可靠性保障。尽管近期研究利用保形预测为机器学习模型构建预测集，但下游决策的关键取决于模型选择。本文针对上下文鲁棒优化提出了新颖的模型选择框架，将鲁棒性控制与决策风险最小化相统一。我们首先提出带模型选择的保形鲁棒优化框架，该框架通过选择模型来近似最小化上下文鲁棒优化解的平均决策风险。针对目标鲁棒性水平1-α，我们提出一种计算高效的E-CROMS算法，能够实现渐近鲁棒性控制与决策最优性。为校正有限样本中的控制偏差，我们进一步开发了两种算法：F-CROMS算法可确保1-α鲁棒性但需遍历标签空间；J-CROMS算法以较低计算成本实现1-2α鲁棒性。此外，我们将CROMS框架扩展至个性化场景，通过最小化给定测试数据协变量的条件决策风险进行模型选择。该框架通过实现协变量感知的模型选择，推动了保形预测方法学的发展。数值实验表明，在多种合成与真实场景应用中，该方法在决策效率上均显著优于基线方法。