Decision-making under uncertainty is hugely important for any decisions sensitive to perturbations in observed data. One method of incorporating uncertainty into making optimal decisions is through robust optimization, which minimizes the worst-case scenario over some uncertainty set. We connect conformal prediction regions to robust optimization, providing finite sample valid and conservative ellipsoidal uncertainty sets, aptly named conformal uncertainty sets. In pursuit of this connection we explicitly define Mahalanobis distance as a potential conformity score in full conformal prediction. We also compare the coverage and optimization performance of conformal uncertainty sets, specifically generated with Mahalanobis distance, to traditional ellipsoidal uncertainty sets on a collection of simulated robust optimization examples.

翻译：将不确定性纳入最佳决策的方法之一是稳健优化,最大限度地减少某些不确定情况中最坏的假设情况。我们将符合要求的预测区域与稳健优化联系起来,提供有限样本的有效和保守的双线性不确定数据组,适当命名为符合要求的不确定数据组。为此,我们明确将马哈拉诺比斯距离定义为完全符合要求的预测中潜在符合标准分数。我们还将符合要求的不确定数据组,特别是用马哈拉诺比斯距离生成的不确定数据组的覆盖范围和最佳性能与收集模拟可靠优化实例的传统的顺线性不确定数据组进行比较。