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

arXiv: https://arxiv.org/abs/2609.16952 · HTML: https://mlsanity.com/paper/2609.16952/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 50 references that are in the map.
- First posted on arXiv 15 Sep 2026.

## Builds on (most cited first, 14 of 14)

- [MurTree: Optimal Classification Trees via Dynamic Programming and Search](https://mlsanity.com/paper/2007.12652/) (2020)
- [Dynamic Pricing in High-dimensions](https://mlsanity.com/paper/1609.07574/) (2016)
- [Decision Trees for Decision-Making under the Predict-then-Optimize Framework](https://mlsanity.com/paper/2003.00360/) (2020)
- [MNL-Bandit: A Dynamic Learning Approach to Assortment Selection](https://mlsanity.com/paper/1706.03880/) (2017)
- [Gap Safe screening rules for sparsity enforcing penalties](https://mlsanity.com/paper/1611.05780/) (2016)
- [Recursive Partitioning for Personalization using Observational Data](https://mlsanity.com/paper/1608.08925/) (2016)
- [Model Distillation for Revenue Optimization: Interpretable Personalized Pricing](https://mlsanity.com/paper/2007.01903/) (2020)
- [Logarithmic Regret in Feature-based Dynamic Pricing](https://mlsanity.com/paper/2102.10221/) (2021)
- [Dynamic pricing and assortment under a contextual MNL demand](https://mlsanity.com/paper/2110.10018/) (2021)
- [The Econometrics of Randomized Experiments](https://mlsanity.com/paper/1607.00698/) (2016)
- [Multi-Product Dynamic Pricing in High-Dimensions with Heterogeneous Price Sensitivity](https://mlsanity.com/paper/1901.01030/) (2019)
- [Outer Approximation With Conic Certificates For Mixed-Integer Convex Problems](https://mlsanity.com/paper/1808.05290/) (2018)
- [Regret Bounds and Experimental Design for Estimate-then-Optimize](https://mlsanity.com/paper/2210.15576/) (2022)
- [Optimal Online and Offline Algorithms for Contextual MNL with Applications to Assortment and Pricing](https://mlsanity.com/paper/2604.19008/) (2026)

## Abstract (arXiv)

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.