学习基于特征的多产品定价的选择模型树：精确优化与实地证据

中文摘要 AI 辅助

基于特征的多产品定价利用客户特征来识别需求异质性，并针对不同产品定制价格。选择模型树通过可解释的特征规则对客户进行细分，并在每个叶节点内拟合需求模型。现有方法通常以贪心方式构建这些树，每次仅选择一个短视的分裂。我们开发了具有多项Logit叶节点的最优选择模型树（OCMT-MNL），在指定深度内联合优化树和叶模型。我们的精确动态规划在约束牛顿迭代期间推导出闭式Fenchel下界，并将其传播到嵌套且不相交的客户子集，避免重新拟合，并在不重复已完成工作的情况下恢复未完成的拟合。在合成实验中，它将精确叶拟合次数减少了99.98%，叶评估次数减少了86.13%，与未剪枝的动态规划相比实现了高达7.15倍的加速。一维查找表将离线估计转化为实时定价，在拟合模型下，收入损失与网格间距呈二次关系。与贪心树相比，OCMT-MNL在合成数据上以更少的叶节点实现更低的收入损失，并在真实数据上实现更好的预测拟合。在一项为期23周、覆盖48个航空市场和190,220名乘客的辅助座位定价随机实验中，OCMT-MNL使每位乘客的座位收入比静态定价显著提高了11.3%。

英文摘要

Feature-based multi-product pricing uses customer characteristics to identify demand heterogeneity and tailor prices across products. Choice model trees segment customers through interpretable feature rules and fit a demand model within each leaf. Existing methods typically construct these trees greedily, selecting one myopic split at a time. We develop optimal choice model trees with multinomial logit leaves (OCMT-MNL), jointly optimizing the tree and leaf models within a prescribed depth. Our exact dynamic program derives closed-form Fenchel lower bounds during constrained Newton iterations and propagates them across nested and disjoint customer subsets, avoiding new fits and resuming unfinished fits without repeating completed work. In synthetic experiments, it reduces exact leaf fits by 99.98% and leaf evaluations by 86.13%, achieving up to 7.15-fold speedups over unpruned dynamic programming. One-dimensional lookup tables translate offline estimation into real-time pricing, with a revenue-loss bound quadratic in grid spacing under the fitted model. Compared with greedy trees, OCMT-MNL achieves lower revenue loss with fewer leaves on synthetic data and better predictive fit on real data. In a 23-week randomized experiment on ancillary seat pricing across 48 airline markets and 190,220 passengers, OCMT-MNL increases seat revenue per passenger by a statistically significant 11.3% over static pricing.

发表机构

• Institute of Operations Research and Analytics, National University of Singapore（新加坡国立大学运筹与分析研究所）
• NUS Business School, National University of Singapore（新加坡国立大学商学院）

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