面向数据驱动决策的Wasserstein歧义集中心与半径学习
Learning the Center and Radius of Wasserstein Ambiguity Sets for Data-Driven Decision Making
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中文总结 AI 辅助
该研究提出了一种灵活的Wasserstein歧义集学习框架，通过预测模型确定名义分布、数据依赖半径，经实验验证可提升决策可靠性，为数据驱动决策提供了新的实用机制。
中文摘要 AI 辅助
Wasserstein分布鲁棒优化（DRO）通常基于经验分布构建，其歧义半径从浓度边界中选取。尽管这种构造提供了有用的统计保证，但它可能过于保守，且无法充分利用潜在分布的预测信息或特定决策问题的难度。我们开发了一个更灵活的框架，其中预测模型确定名义分布，另一个单独的模型估计依赖于数据的半径。关键要求并非歧义集以经验分布为中心，而是它以期望概率包含未知的数据生成分布。我们为任意学习到的中心建立了有限样本保证和渐近一致性，为非均匀离散预测分布推导了可处理的重新表述，分离了预测模型和场景离散化误差，并证明了在中心和半径同时扰动下的稳定性。我们进一步将神条件分位数半径表征为最小的条件有效规则，并引入了一种分裂共形程序用于有限样本边际校准。对报童问题、合成投资组合、分布偏移和真实金融数据的实验表明，学习和校准后的歧义集可提高可靠性，但不会自动产生更小的半径或更好的决策。总体而言，所提出的框架将校准视为可靠决策的实用机制，而非优化性能提升的普遍保证。
英文摘要
Wasserstein distributionally robust optimization (DRO) is commonly built around the empirical distribution, with the ambiguity radius selected from a concentration bound. Although this construction provides useful statistical guarantees, it can be conservative and does not fully exploit predictive information about the underlying distribution or the difficulty of a particular decision problem. We develop a more flexible framework in which a predictive model determines the nominal distribution and a separate model estimates a data-dependent radius. The key requirement is not that the ambiguity set be centered at the empirical distribution, but that it contain the unknown data-generating distribution with the desired probability. We establish finite-sample guarantees and asymptotic consistency for arbitrary learned centers, derive tractable reformulations for non-uniform discrete predictive distributions, separate predictive-model and scenario-discretization errors, and prove stability under simultaneous perturbations of the center and radius. We further characterize the oracle conditional-quantile radius as the smallest conditionally valid rule and introduce a split-conformal procedure for finite-sample marginal calibration. Experiments on newsvendor problems, synthetic portfolios, distribution shifts, and real financial data show that learned and calibrated ambiguity sets can improve reliability, but do not automatically yield smaller radii or better decisions. Overall, the proposed framework treats calibration as a practical mechanism for reliable decision making rather than a universal guarantee of improved optimization performance.
