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

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 singlemindedly 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. The key here is that a low-cost surrogate function can be an accurate proxy for the very computationally costly optimal tree in terms of expected regret. This surrogate can be fit many times with different hyperparameter values to proxy the performance of the optimal model. The method is applied to a real-world case-study of conditional cash transfers in Morocco where hybrid (partially optimal, partially greedy) policy trees provide good performance as a surrogate for optimal trees while being computationally cheap enough to feasibly fit a Pareto frontier.