通过诊断传输校准歧义集以实现分布鲁棒优化

中文摘要 AI 辅助

分布鲁棒优化（DRO）通过在歧义集上进行优化来保护决策免受分布不确定性的影响，但几何结构不匹配的歧义集往往需要较大的半径，导致决策过于保守。我们提出诊断传输分布鲁棒优化（DT-DRO），利用预留的校准数据使歧义集的几何结构适配观测到的预测误差。DT-DRO采用条件概率积分变换累积分布函数诊断系统性概率分配偏差，并将该信息转化为结果级传输，同时调整歧义集中心和基础成本。该公式可得到计算上易处理的对偶重构。理论上，我们推导了有效的歧义半径和决策风险保证，其会随估计误差和近似误差消失而收紧，且DT-DRO可消除由模型误设导致的非零鲁棒性下限。合成实验和停电应用表明，该方法能提升决策质量，尤其在结构误设和尾部误设场景下表现突出。

英文摘要

Distributionally robust optimization (DRO) protects decisions against distributional uncertainty by optimizing over an ambiguity set, but poorly aligned set geometry can require large radii and yield overly conservative decisions. We introduce diagnostic-transport DRO (DT-DRO), which uses held-out calibration data to adapt the ambiguity-set geometry to observed predictive errors. DT-DRO uses the conditional probability integral transform cumulative distribution function to diagnose systematic probability misallocation and translates this information into an outcome-level transport that jointly adjusts the ambiguity-set center and ground cost. The resulting formulation admits a computationally tractable dual reformulation. Theoretically, we derive valid ambiguity radii and decision-risk guarantees that tighten as estimation and approximation errors vanish, and show that DT-DRO can eliminate the nonvanishing robustness floor caused by model misspecification. Synthetic experiments and a power-outage application demonstrate improved decision quality, particularly under structural and tail misspecification.

发表机构

• Heinz College of Information Systems and Public Policy, Carnegie Mellon University（卡内基梅隆大学海因茨信息系统与公共政策学院）
• Machine Learning Department, Carnegie Mellon University（卡内基梅隆大学机器学习系）
• Department of Statistics and Data Science, Carnegie Mellon University（卡内基梅隆大学统计与数据科学系）

机构由 AI 辅助整理，请以论文原文为准。