# Constrained Prescriptive Trees via Column Generation

arXiv: https://arxiv.org/abs/2207.10163 · HTML: https://mlsanity.com/paper/2207.10163/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 48 references that are in the map.
- First posted on arXiv 20 Jul 2022.

## Builds on (most cited first, 18 of 18)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Distilling a Neural Network Into a Soft Decision Tree](https://mlsanity.com/paper/1711.09784/) (2017)
- [Explainable Reinforcement Learning: A Survey](https://mlsanity.com/paper/2005.06247/) (2020)
- [Learning Optimal and Fair Decision Trees for Non-Discriminative Decision-Making](https://mlsanity.com/paper/1903.10598/) (2019)
- [Toward Interpretable Deep Reinforcement Learning with Linear Model U-Trees](https://mlsanity.com/paper/1807.05887/) (2018)
- [Offline Multi-Action Policy Learning: Generalization and Optimization](https://mlsanity.com/paper/1810.04778/) (2018)
- [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)
- [A Scalable MIP-based Method for Learning Optimal Multivariate Decision Trees](https://mlsanity.com/paper/2011.03375/) (2020)
- [Optimal Policy Trees](https://mlsanity.com/paper/2012.02279/) (2020)
- [Learning Optimal Classification Trees: Strong Max-Flow Formulations](https://mlsanity.com/paper/2002.09142/) (2020)

## Built on by (most cited first, 6 of 6)

- [Scalable Optimal Multiway-Split Decision Trees with Constraints](https://mlsanity.com/paper/2302.06812/) (2023)
- [Learning Prescriptive ReLU Networks](https://mlsanity.com/paper/2306.00651/) (2023)
- [PresAIse, A Prescriptive AI Solution for Enterprises](https://mlsanity.com/paper/2402.02006/) (2024)
- [Robust personalized pricing under uncertainty of purchase probabilities](https://mlsanity.com/paper/2407.15332/) (2024)
- [The Value of AI Advice: Personalized and Value-Maximizing AI Advisors Are Necessary to Reliably Benefit Experts and Organizations](https://mlsanity.com/paper/2412.19530/) (2024)
- [Constrained Triple-Head Price Optimization (C3PO) Network for Discrete-Choice Models](https://mlsanity.com/paper/2605.06941/) (2026)

## Abstract (arXiv)

With the abundance of available data, many enterprises seek to implement data-driven prescriptive analytics to help them make informed decisions. These prescriptive policies need to satisfy operational constraints, and proactively eliminate rule conflicts, both of which are ubiquitous in practice. It is also desirable for them to be simple and interpretable, so they can be easily verified and implemented. Existing approaches from the literature center around constructing variants of prescriptive decision trees to generate interpretable policies. However, none of the existing methods are able to handle constraints. In this paper, we propose a scalable method that solves the constrained prescriptive policy generation problem. We introduce a novel path-based mixed-integer program (MIP) formulation which identifies a (near) optimal policy efficiently via column generation. The policy generated can be represented as a multiway-split tree which is more interpretable and informative than a binary-split tree due to its shorter rules. We demonstrate the efficacy of our method with extensive experiments on both synthetic and real datasets.