提出可快速计算的鲁棒优化框架,解决数据污染下的决策失效问题。
Bulk-Calibrated Credal Ambiguity Sets: Fast, Tractable Decision Making under Out-of-Sample Contamination
- 基于数据学习主体分布,分别处理内部污染与尾部异常
- 得到闭式解且风险有限,支持线性/二阶锥规划求解
- 适用于库存、房价、文本等场景,兼具效率与鲁棒性
分布鲁棒优化(DRO)通过在不确定性集上最小化最坏情况期望损失来应对样本外分布偏移。尽管Huber(线性空洞)污染模型以最小假设描述ε比例的任意扰动,但将其纳入不确定性集可能导致最坏风险无穷大,使DRO目标失效,除非施加强制的有界性或支撑集假设。本文提出批量校准的可信不确定性集:从数据中学习高概率主体集,同时考虑主体内的污染,并单独限制剩余尾部贡献。该方法导出闭式、有限的均值+上确界鲁棒目标,对常见损失函数和主体几何结构可转化为可处理的线性或二阶锥规划。通过此框架,揭示了模糊概率(IP)中的上期望与最坏风险之间的等价性,展示了如何将IP可信集转化为具有可解释容忍度的DRO目标。在重尾库存控制、地理迁移的房价回归、人口结构迁移的文本分类实验中,该方法展现出竞争性的鲁棒-精度权衡和高效的优化时间,可使用贝叶斯、频率论或经验参考分布。
原文摘要 · Abstract (English)
Distributionally robust optimisation (DRO) minimises the worst-case expected loss over an ambiguity set that can capture distributional shifts in out-of-sample environments. While Huber (linear-vacuous) contamination is a classical minimal-assumption model for an $\varepsilon$-fraction of arbitrary perturbations, including it in an ambiguity set can make the worst-case risk infinite and the DRO objective vacuous unless one imposes strong boundedness or support assumptions. We address these challenges by introducing bulk-calibrated credal ambiguity sets: we learn a high-mass bulk set from data while considering contamination inside the bulk and bounding the remaining tail contribution separately. This leads to a closed-form, finite $\mathrm{mean}+\sup$ robust objective and tractable linear or second-order cone programs for common losses and bulk geometries. Through this framework, we highlight and exploit the equivalence between the imprecise probability (IP) notion of upper expectation and the worst-case risk, demonstrating how IP credal sets translate into DRO objectives with interpretable tolerance levels. Experiments on heavy-tailed inventory control, geographically shifted house-price regression, and demographically shifted text classification show competitive robustness-accuracy trade-offs and efficient optimisation times, using Bayesian, frequentist, or empirical reference distributions.
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