Nonparametric Bayesian Policy Learning

Abstract

I propose Nonparametric Bayesian Policy Learning (NBPL) as a framework for uncertainty-aware treatment choice. I consider a decision-maker (DM) seeking to select an expected welfare-maximizing treatment rule using observable characteristics. A key observation is that, for a given welfare criterion and policy class, uncertainty about welfare-relevant objects is entirely induced by uncertainty about a reduced-form distribution. I assume the DM places a nonparametric Dirichlet process prior on this reduced-form parameter and uses the resulting posterior to conduct inference on optimal treatment assignments, optimal welfare, and comparisons across policy classes. The NBPL framework is flexible, and its implementation via the Bayesian bootstrap is highly tractable. I establish two main theoretical properties of NBPL. First, posterior welfare regret under NBPL converges at the minimax-optimal rate. Second, posterior model comparison across policy classes is pointwise consistent. I illustrate NBPL in two empirical applications: the bednet subsidy experiment of Bhattacharya and Dupas (2012) and the JTPA experiment studied by Kitagawa and Tetenov (2018).