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 than existing approaches. These results offer the first principled data-driven methodology for guiding robustness selection and empower 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场景进行优化来保护决策免受不确定性影响，然而其有效性依赖于预先指定的鲁棒性水平，该水平通常被随意选择，导致保护不足或解决方案过于保守且成本高昂。近期利用保形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合，但它们仍先验固定覆盖目标，且对鲁棒性水平的选择缺乏指导。我们提出一个新框架，为任何鲁棒预测-优化策略族提供关于误覆盖和遗憾的分布无关有限样本保证。我们的方法构建了能追踪误覆盖-遗憾帕累托前沿的有效估计器，使决策者能够根据其成本-风险偏好可靠评估和校准鲁棒性水平。该框架易于实现，广泛适用于经典优化公式，且比现有方法获得更优的有限样本性能。这些成果首次提供了指导鲁棒性选择的原理性数据驱动方法，使实践者能够在高风险决策中平衡鲁棒性与保守性。