We study the feature-based newsvendor problem, in which a decision-maker has access to historical data consisting of demand observations and exogenous features. In this setting, we investigate feature selection, aiming to derive sparse, explainable models with improved out-of-sample performance. Up to now, state-of-the-art methods utilize regularization, which penalizes the number of selected features or the norm of the solution vector. As an alternative, we introduce a novel bilevel programming formulation. The upper-level problem selects a subset of features that minimizes an estimate of the out-of-sample cost of ordering decisions based on a held-out validation set. The lower-level problem learns the optimal coefficients of the decision function on a training set, using only the features selected by the upper-level. We present a mixed integer linear program reformulation for the bilevel program, which can be solved to optimality with standard optimization solvers. Our computational experiments show that the method accurately recovers ground-truth features already for instances with a sample size of a few hundred observations. In contrast, regularization-based techniques often fail at feature recovery or require thousands of observations to obtain similar accuracy. Regarding out-of-sample generalization, we achieve improved or comparable cost performance.
翻译:我们研究基于地貌的Newsvendor问题, 即决策者能够获得由需求观测和外源特征组成的历史数据。 在这种环境下, 我们调查地物选择, 目的是获得稀少的、可解释的模型, 改进外表性能。 到目前为止, 最先进的方法使用正规化方法, 惩罚选定特性的数量或解决方案矢量的规范。 作为替代办法, 我们引入一个新的双级编程配方。 高层问题选择了一组特征, 将根据固定验证集进行决策的外部成本估计降到最低。 较低层次的问题只利用高层次所选的特征, 了解一套培训集决策功能的最佳系数。 我们为双层程序提出了一个混合整数线性方案, 它可以用标准优化解决方案解决方案解决。 我们的计算实验显示, 这种方法准确恢复了已经存在几百个观察样本的地底线性特征。 相反, 基于正规化的技术往往无法在地貌恢复或可比较性能方面实现类似的精确性。