# Learning Prescriptive ReLU Networks

arXiv: https://arxiv.org/abs/2306.00651 · HTML: https://mlsanity.com/paper/2306.00651/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 53 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Understanding Deep Neural Networks with Rectified Linear Units](https://mlsanity.com/paper/1611.01491/) (2016)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Bounding and Counting Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1711.02114/) (2017)
- [Deep ReLU Networks Have Surprisingly Few Activation Patterns](https://mlsanity.com/paper/1906.00904/) (2019)
- [Strong mixed-integer programming formulations for trained neural networks](https://mlsanity.com/paper/1811.08359/) (2018)
- [Offline Multi-Action Policy Learning: Generalization and Optimization](https://mlsanity.com/paper/1810.04778/) (2018)
- [Some methods for heterogeneous treatment effect estimation in high-dimensions](https://mlsanity.com/paper/1707.00102/) (2017)
- [Learning Sparse Networks Using Targeted Dropout](https://mlsanity.com/paper/1905.13678/) (2019)
- [Lossless Compression of Deep Neural Networks](https://mlsanity.com/paper/2001.00218/) (2020)
- [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)
- [Towards Robust, Locally Linear Deep Networks](https://mlsanity.com/paper/1907.03207/) (2019)
- [Optimal Policy Trees](https://mlsanity.com/paper/2012.02279/) (2020)
- [Efficient non-greedy optimization of decision trees](https://mlsanity.com/paper/1511.04056/) (2015)
- [Oblique Decision Trees from Derivatives of ReLU Networks](https://mlsanity.com/paper/1909.13488/) (2019)
- [Optimizing Objective Functions from Trained ReLU Neural Networks via Sampling](https://mlsanity.com/paper/2205.14189/) (2022)
- [Scalable Optimal Multiway-Split Decision Trees with Constraints](https://mlsanity.com/paper/2302.06812/) (2023)
- [Loss Functions for Discrete Contextual Pricing with Observational Data](https://mlsanity.com/paper/2111.09933/) (2021)
- [Constrained Prescriptive Trees via Column Generation](https://mlsanity.com/paper/2207.10163/) (2022)

## Built on by (most cited first, 1 of 1)

- [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)

## Abstract (arXiv)

We study the problem of learning optimal policy from a set of discrete treatment options using observational data. We propose a piecewise linear neural network model that can balance strong prescriptive performance and interpretability, which we refer to as the prescriptive ReLU network, or P-ReLU. We show analytically that this model (i) partitions the input space into disjoint polyhedra, where all instances that belong to the same partition receive the same treatment, and (ii) can be converted into an equivalent prescriptive tree with hyperplane splits for interpretability. We demonstrate the flexibility of the P-ReLU network as constraints can be easily incorporated with minor modifications to the architecture. Through experiments, we validate the superior prescriptive accuracy of P-ReLU against competing benchmarks. Lastly, we present examples of interpretable prescriptive trees extracted from trained P-ReLUs using a real-world dataset, for both the unconstrained and constrained scenarios.