发表机构
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对基于特征的报童模型变量选择问题，在硬基数约束下构建带正则化的优化模型，提出高效算法并通过实验验证其在减少协变量数量的同时保持竞争力运营成本的优势。
AI 中文摘要
基于特征的报童模型使用可观测协变量来定制库存决策，旨在平衡需求不确定性下的持有成本与缺货成本。然而，高维特征集常阻碍可解释性，并增加数据收集与实施成本。本文研究在所选特征数量的硬基数约束下，基于特征的报童问题的变量选择，构建带ℓ₂正则化的ℓ₀约束经验报童问题，明确其计算复杂性，提出混合整数二阶锥规划重构方法，该方法强化了标准Big-M重构。为实现超出精确优化的可扩展性，开发带双准则保证的随机舍入算法及贪心启发式算法。统计层面，对所得稀疏策略估计量提供理论分析，包括有限样本估计误差、样本外风险边界及支持集恢复保证。在合成与真实数据上的大量实验，展示了各基线间的计算与统计权衡，结果表明，所提变量选择框架在使用显著更少协变量的同时，实现了具竞争力的样本外运营成本。
英文摘要
Feature-based newsvendor models use observable covariates to tailor inventory decisions, aiming to balance holding and shortage costs under demand uncertainty. However, high-dimensional feature sets often hinder interpretability and inflate data collection and implementation costs. This paper studies variable selection for the feature-based newsvendor problem under a hard cardinality constraint on the number of selected features. We formulate the resulting $\ell_0$-constrained empirical newsvendor problem with $\ell_2$-regularization, establish its computational hardness, and develop a mixed-integer second-order cone programming reformulation that strengthens the standard Big-$M$ formulation. To enable scalability beyond exact optimization, we develop a randomized-rounding algorithm with a bi-criteria guarantee and a greedy heuristic. Statistically, we provide theoretical analysis of the resulting sparse policy estimator, including finite-sample estimation error, out-of-sample risk bounds, and support recovery guarantees. Extensive experiments on both synthetic and real data illustrate the computational and statistical trade-offs among various baselines. Our results demonstrate that the proposed variable selection framework achieves competitive out-of-sample operational costs while using substantially fewer covariates.
