Learning Choice Model Trees for Feature-Based Multi-Product Pricing: Exact Optimization and Field Evidence

2026-09-15

AI Summary

本文提出了一种最优选择模型树(OCMT-MNL)，通过联合优化树结构和叶节点模型来解决基于特征的多产品定价问题，相比贪婪算法，在合成数据和实际应用中均表现更优。

Abstract

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.

Problem

• Feature-based multi-product pricing
• Choice model trees
• Demand heterogeneity
• Multinomial logit

Innovation

• Optimal Choice Model Trees
• Multinomial Logit Leaves
• Dynamic Programming
• Fenchel Lower Bounds
• Real-time Pricing