Bandit algorithms for policy learning: methods, implementation, and welfare-performance

Abstract

Static supervised learning—in which experimental data serves as a training sample for the estimation of an optimal treatment assignment policy—is a commonly assumed framework of policy learning. An arguably more realistic but challenging scenario is a dynamic setting in which the planner performs experimentation and exploitation simultaneously with subjects that arrive sequentially. This paper studies bandit algorithms for learning an optimal individualised treatment assignment policy. Specifically, we study applicability of the EXP4.P (Exponential weighting for Exploration and Exploitation with Experts) algorithm developed by Beygelzimer et al. (Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics, JMLR Workshop and Conference Proceedings, pp 19–26, 2011) to policy learning. Assuming that the class of policies has a finite Vapnik–Chervonenkis dimension and that the number of subjects to be allocated is known, we present a high probability welfare-regret bound of the algorithm. To implement the algorithm, we use an incremental enumeration algorithm for hyperplane arrangements. We perform extensive numerical analysis to assess the algorithm’s sensitivity to its tuning parameters and its welfare-regret performance. Further simulation exercises are calibrated to the National Job Training Partnership Act (JTPA) Study sample to determine how the algorithm performs when applied to economic data. Our findings highlight various computational challenges and suggest that the limited welfare gain from the algorithm is due to substantial heterogeneity in causal effects in the JTPA data.