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There has recently been a considerable amount of work on statistical methodology for policy learning, including Manski (2004), Zhao, Zeng, Rush, & Kosorok (2012), Swaminathan & Joachims (2015), Kitagawa & Tetenov (2018), van der Laan & Luedtke (2015), Luedtke & van der Laan (2016), Mbakop & Tabord-Meehan (2016), Athey & Wager (2017), Kallus & Zhou (2018), and Zhou, Athey, & Wager (2018). In particular, Kitagawa & Tetenov (2018) show that if we only consider policies π restricted to a class Π with finite VC dimension and have access to data from a randomized trial with n samples, then an empirical welfare maximization algorithm achieves regret that scales as √ VC(Π)/n. Athey & Wager (2017) extend this result to observational studies via doubly robust scoring, and Zhou et al. (2018) further consider the case with multiple treatment choices (in particular, the regret will depend on the tree depth, feature space, and number of actions).

policytree: Policy learning via doubly robust empirical welfare maximization over trees