Optimal sequential decision-making with initiation regimes
Consider an optimal dynamic treatment regime, $g^{\textbf{opt}}$ correctly identified from a large, perfectly executed sequentially randomized experiment. Even when the experimental results are generalizable to a future target population, there is no guarantee that $g^{\textbf{opt}}$ outperforms human decision-makers; human experts can do better than $g^{\textbf{opt}}$ whenever they have access to relevant information beyond the covariates recorded in the experiment. Motivated by this observation, we derive results on a new class of regimes called initiation regimes, which generalize existing results on superoptimal regimes. These regimes follow human decision-makers up to the point where it becomes more beneficial to initiate a sequential optimal regime, and are guaranteed to outperform both purely human and purely algorithmic decision rules, e.g., based on reinforcement learning algorithms. Furthermore, we present modified experimental designs that identify the best initiation regimes, show how the best initiation regime can be identified from classical observational data under explicit assumptions, and give estimation and statistical inference methodology for these regimes. To illustrate the practical utility of the methods, we consider initiation regimes in a case study on treatment of lower back pain.