# Learning Optimal Prescriptive Trees from Observational Data

arXiv: https://arxiv.org/abs/2108.13628 · HTML: https://mlsanity.com/paper/2108.13628/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 78 references that are in the map.
- First posted on arXiv 31 Aug 2021.

## Builds on (most cited first, 21 of 21)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Learning Optimal and Fair Decision Trees for Non-Discriminative Decision-Making](https://mlsanity.com/paper/1903.10598/) (2019)
- [Offline Multi-Action Policy Learning: Generalization and Optimization](https://mlsanity.com/paper/1810.04778/) (2018)
- [Decision Trees for Decision-Making under the Predict-then-Optimize Framework](https://mlsanity.com/paper/2003.00360/) (2020)
- [Balanced Policy Evaluation and Learning](https://mlsanity.com/paper/1705.07384/) (2017)
- [The Convex Relaxation Barrier, Revisited: Tightened Single-Neuron Relaxations for Neural Network Verification](https://mlsanity.com/paper/2006.14076/) (2020)
- [Some methods for heterogeneous treatment effect estimation in high-dimensions](https://mlsanity.com/paper/1707.00102/) (2017)
- [Sparse Regression at Scale: Branch-and-Bound rooted in First-Order Optimization](https://mlsanity.com/paper/2004.06152/) (2020)
- [Sparse High-Dimensional Regression: Exact Scalable Algorithms and Phase Transitions](https://mlsanity.com/paper/1709.10029/) (2017)
- [Recursive Partitioning for Personalization using Observational Data](https://mlsanity.com/paper/1608.08925/) (2016)
- [Strong Optimal Classification Trees](https://mlsanity.com/paper/2103.15965/) (2021)
- [Optimization of Tree Ensembles](https://mlsanity.com/paper/1705.10883/) (2017)
- [The ALAMO approach to machine learning](https://mlsanity.com/paper/1705.10918/) (2017)
- [Combinatorial Attacks on Binarized Neural Networks](https://mlsanity.com/paper/1810.03538/) (2018)
- [Behavioral Analytics for Myopic Agents](https://mlsanity.com/paper/1702.05496/) (2017)
- [Spectral Algorithms for Computing Fair Support Vector Machines](https://mlsanity.com/paper/1710.05895/) (2017)
- [Optimal Generalized Decision Trees via Integer Programming](https://mlsanity.com/paper/1612.03225/) (2016)
- [Optimal Multilevel Matching in Clustered Observational Studies: A Case Study of the Effectiveness of Private Schools Under a Large-Scale Voucher System](https://mlsanity.com/paper/1409.8597/) (2014)

## Built on by (most cited first, 10 of 10)

- [Learning Optimal Fair Classification Trees: Trade-offs Between Interpretability, Fairness, and Accuracy](https://mlsanity.com/paper/2201.09932/) (2022)
- [Optimal or Greedy Decision Trees? Revisiting their Objectives, Tuning, and Performance](https://mlsanity.com/paper/2409.12788/) (2024)
- [Learning Resource Allocation Policies from Observational Data with an Application to Homeless Services Delivery](https://mlsanity.com/paper/2201.10053/) (2022)
- [Interpretable Personalized Experimentation](https://mlsanity.com/paper/2111.03267/) (2021)
- [Learning Optimal Classification Trees Robust to Distribution Shifts](https://mlsanity.com/paper/2310.17772/) (2023)
- [Learning Fair Policies for Multi-stage Selection Problems from Observational Data](https://mlsanity.com/paper/2312.13173/) (2023)
- [Feature-Based Interpretable Surrogates for Optimization](https://mlsanity.com/paper/2409.01869/) (2024)
- [PresAIse, A Prescriptive AI Solution for Enterprises](https://mlsanity.com/paper/2402.02006/) (2024)
- [Applications of 0-1 Neural Networks in Prescription and Prediction](https://mlsanity.com/paper/2402.18851/) (2024)
- [Counterfactual Optimal Action Trees (COAT): Interpretable Prescriptive Policies from Observational Data](https://mlsanity.com/paper/2607.14318/) (2026)

## Abstract (arXiv)

We consider the problem of learning an optimal prescriptive tree (i.e., an interpretable treatment assignment policy in the form of a binary tree) of moderate depth, from observational data. This problem arises in numerous socially important domains such as public health and personalized medicine, where interpretable and data-driven interventions are sought based on data gathered in deployment -- through passive collection of data -- rather than from randomized trials. We propose a method for learning optimal prescriptive trees using mixed-integer optimization (MIO) technology. We show that under mild conditions our method is asymptotically exact in the sense that it converges to an optimal out-of-sample treatment assignment policy as the number of historical data samples tends to infinity. Contrary to existing literature, our approach: 1) does not require data to be randomized, 2) does not impose stringent assumptions on the learned trees, and 3) has the ability to model domain specific constraints. Through extensive computational experiments, we demonstrate that our asymptotic guarantees translate to significant performance improvements in finite samples, as well as showcase our uniquely flexible modeling power by incorporating budget and fairness constraints.