# Policy learning for many outcomes of interest: Combining optimal policy trees with multi-objective Bayesian optimisation

arXiv: https://arxiv.org/abs/2212.06312 · HTML: https://mlsanity.com/paper/2212.06312/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 75 references that are in the map.
- First posted on arXiv 13 Dec 2022.

## Builds on (most cited first, 20 of 20)

- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [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)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2006.05078/) (2020)
- [Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvement](https://mlsanity.com/paper/2105.08195/) (2021)
- [Optimal Sparse Decision Trees](https://mlsanity.com/paper/1904.12847/) (2019)
- [Confounding-Robust Policy Improvement](https://mlsanity.com/paper/1805.08593/) (2018)
- [Offline Multi-Action Policy Learning: Generalization and Optimization](https://mlsanity.com/paper/1810.04778/) (2018)
- [Estimating Treatment Effects with Causal Forests: An Application](https://mlsanity.com/paper/1902.07409/) (2019)
- [Fast Sparse Decision Tree Optimization via Reference Ensembles](https://mlsanity.com/paper/2112.00798/) (2021)
- [Recursive Partitioning for Personalization using Observational Data](https://mlsanity.com/paper/1608.08925/) (2016)
- [A survey on multi-objective hyperparameter optimization algorithms for Machine Learning](https://mlsanity.com/paper/2111.13755/) (2021)
- [Optimal Policy Trees](https://mlsanity.com/paper/2012.02279/) (2020)
- [Assessing Treatment Effect Variation in Observational Studies: Results from a Data Challenge](https://mlsanity.com/paper/1907.07592/) (2019)
- [Machine learning for causal inference: on the use of cross-fit estimators](https://mlsanity.com/paper/2004.10337/) (2020)
- [The Infinitesimal Jackknife and Combinations of Models](https://mlsanity.com/paper/2209.00147/) (2022)
- [Nonparametric Heterogeneous Treatment Effect Estimation in Repeated Cross Sectional Designs](https://mlsanity.com/paper/1905.11622/) (2019)

## Abstract (arXiv)

Methods for learning optimal policies use causal machine learning models to create human-interpretable rules for making choices around the allocation of different policy interventions. However, in realistic policy-making contexts, decision-makers often care about trade-offs between outcomes, not just single-mindedly maximising utility for one outcome. This paper proposes an approach termed Multi-Objective Policy Learning (MOPoL) which combines optimal decision trees for policy learning with a multi-objective Bayesian optimisation approach to explore the trade-off between multiple outcomes. It does this by building a Pareto frontier of non-dominated models for different hyperparameter settings which govern outcome weighting. The key here is that a low-cost greedy tree can be an accurate proxy for the very computationally costly optimal tree for the purposes of making decisions which means models can be repeatedly fit to learn a Pareto frontier. The method is applied to a real-world case-study of non-price rationing of anti-malarial medication in Kenya.