Robust optimization safeguards decisions against uncertainty by optimizing against worst-case scenarios, yet their effectiveness hinges on a prespecified robustness level that is often chosen ad hoc, leading to either insufficient protection or overly conservative and costly solutions. Recent approaches using conformal prediction construct data-driven uncertainty sets with finite-sample coverage guarantees, but they still fix coverage targets a priori and offer little guidance for selecting robustness levels. We propose a new framework that provides distribution-free, finite-sample guarantees on both miscoverage and regret for any family of robust predict-then-optimize policies. Our method constructs valid estimators that trace out the miscoverage--regret Pareto frontier, enabling decision-makers to reliably evaluate and calibrate robustness levels according to their cost--risk preferences. The framework is simple to implement, broadly applicable across classical optimization formulations, and achieves sharper finite-sample performance. This paper offers a principled data-driven methodology for guiding robustness selection and empowers practitioners to balance robustness and conservativeness in high-stakes decision-making.

翻译：鲁棒优化通过针对最坏情况进行优化来保障决策免受不确定性影响，但其效果取决于预先指定的鲁棒性水平——这一水平通常凭经验随意设定，导致要么保护不足，要么因过度保守而产生高昂代价。近期基于保序预测的方法构建了具有有限样本覆盖保证的数据驱动不确定性集，但这些方法仍先验地固定覆盖目标，对鲁棒性水平的选择缺乏指导。本文提出一种新框架，为任意一类鲁棒"预测-优化"策略提供关于误覆盖率和遗憾值的无分布、有限样本保证。该方法构造出可勾勒误覆盖率-遗憾值帕累托前沿的有效估计量，使决策者能够根据其成本-风险偏好可靠地评估和校准鲁棒性水平。该框架实现简便，广泛适用于经典优化形式，且具有更优的有限样本性能。本文为引导鲁棒性选择提供了原则性的数据驱动方法论，使实践者能够在高风险决策中平衡鲁棒性与保守性。