No abstract

In this section, we include additional simulation results to further demonstrate the performance of our methods. Continuous Outcome StudiesWhen the clinical outcome R is continuous, we report the simulation results with n = 400, 800, p = 20 and n = 200, p = 20, 40 for the three continuous simulation scenarios in the main paper.

Recent development in the data-driven decision science has seen great advances in individualized decision making. Given data with individual covariates, treatment assignments and outcomes, policy makers best individualized treatment rule (ITR) that maximizes the expected outcome, known as the value function. Many existing methods assume that the training and testing distributions are the same. However, the estimated optimal ITR may have poor generalizability when the training and testing distributions are not identical. In this article, we consider the problem of finding an optimal ITR from a restricted ITR class where there are some unknown covariate changes between the training and testing distributions. We propose a novel distributionally robust ITR (DR-ITR) framework that maximizes the worst-case value function across the values under a set of underlying distributions that are "close" to the training distribution. The resulting DR-ITR can guarantee the performance among all such distributions reasonably well. We further propose a calibrating procedure that tunes the DR-ITR adaptively to a small amount of calibration data from a target population. In this way, the calibrated DR-ITR can be shown to enjoy better generalizability than the standard ITR based on our numerical studies. Supplementary materials for this article are available online.

We consider the batch (off-line) policy learning problem in the infinite horizon Markov Decision Process. Motivated by mobile health applications, we focus on learning a policy that maximizes the longterm average reward. We propose a doubly robust estimator for the average reward and show that it achieves semiparametric efficiency given multiple trajectories collected under some behavior policy. Based on the proposed estimator, we develop an optimization algorithm to compute the optimal policy in a parameterized stochastic policy class. The performance of the estimated policy is measured by the difference between the optimal average reward in the policy class and the average reward of the estimated policy and we establish a finite-sample regret guarantee. To the best of our knowledge, this is the first regret bound for batch policy learning in the infinite time horizon setting. The performance of the method is illustrated by simulation studies.