发表机构
Tsinghua University; University of Toronto; McGill University（清华大学; 多伦多大学; 麦吉尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于共形分数的鲁棒性框架，将黑箱预测器转化为决策相关的不确定性表示，统一可靠性与目标导向优化，实现可靠性保证和脆弱性分析。
AI 中文摘要
现代预测驱动的决策系统通常依赖黑箱预测器，但仅有点预测并不能提供下游稳健决策所需的不确定性尺度。我们构建了一个分数校准的鲁棒性框架，通过无分布的共形校准，将任意固定点预测器转换为与决策相关的不确定性表示。我们使用共形分数，而非特定的不确定性集合，作为鲁棒性的基本单元。同一分数既确定了用于基于可靠性的鲁棒优化的覆盖校准不确定性集合，又在目标导向的公式——共形鲁棒满足——中归一化目标违规。该公式引入了一种共形脆弱性度量，用于量化当实现参数在共形分数尺度上偏离预测时，性能恶化的速度。对于在标准凸性和对偶条件下的目标不确定性问题，我们证明了基于可靠性和目标导向的公式参数化了相同的分数校准鲁棒决策前沿。这一等价性产生了可靠性水平与可接受目标之间的数据驱动映射，并刻画了鲁棒性的边际成本。合成实验验证了理论保证，并说明了可靠性-目标的对应关系。一项真实数据的在线杂货案例研究展示了该接口如何将深度学习需求预测与易处理的库存优化相结合，从而提高可靠性并降低运营成本。总体而言，我们的工作表明，共形分数赋予固定黑箱预测器一个可解释的不确定性尺度，用于下游决策，同时在统一框架内实现可靠性保证、可接受目标选择和脆弱性分析。
英文摘要
Modern prediction-driven decision systems often rely on black-box predictors, but a point forecast alone does not provide the uncertainty scale required for robust downstream decision-making. We build a score-calibrated robustness framework that converts any fixed point predictor into a decision-relevant uncertainty representation through distribution-free conformal calibration. We use the conformal score, rather than a particular uncertainty set, as the primitive unit of robustness. The same score determines coverage-calibrated uncertainty sets for reliability-based robust optimization and normalizes target violations in a target-oriented formulation, Conformal Robust Satisficing. This formulation induces a conformal fragility measure that quantifies how rapidly performance deteriorates as the realized parameter departs from the forecast on the conformal score scale. For objective-uncertainty problems under standard convexity and duality conditions, we show that the reliability-based and target-oriented formulations parameterize the same score-calibrated robust decision frontier. This equivalence yields a data-driven mapping between reliability levels and acceptable targets and characterizes the marginal cost of robustness. Synthetic experiments validate the theoretical guarantees and illustrate the reliability-target correspondence. A real-data online-grocery case study demonstrates how the interface combines deep-learning demand forecasts with tractable inventory optimization, thereby improving reliability and reducing operational costs. Overall, our work shows that conformal scores endow fixed black-box predictors with an interpretable uncertainty scale for downstream decision-making while enabling reliability guarantees, acceptable-target selection, and fragility analysis within a unified framework.
