Optimal Prescriptive Trees

Motivated by personalized decision making, given observational data ${\left\{\left({\mathbf{x}}_i,y_i,z_i\right)\right\}}_{i=1}^n$ involving features ${\mathbf{x}}_i\in {\mathbb{R}}^d$, assigned treatments or prescriptions $z_i\in \left\{1,\dots ,m\right\}$, and outcomes $y_i\in \mathbb{R}$, we propose a tree-based algorithm called optimal prescriptive tree (OPT) that uses either constant or linear models in the leaves of the tree to predict the counterfactuals and assign optimal treatments to new samples. We propose an objective function that balances optimality and accuracy. OPTs are interpretable and highly scalable, accommodate multiple treatments, and provide high-quality prescriptions. We report results involving synthetic and real data that show that OPTs either outperform or are comparable with several state-of-the-art methods. Given their combination of interpretability, scalability, generalizability, and performance, OPTs are an attractive alternative for personalized decision making in a variety of areas, such as online advertising and personalized medicine.