Robust Learning for Optimal Dynamic Treatment Regimes with Observational Data

Public policies and medical interventions often involve dynamics in their treatment assignments, where individuals receive a series of interventions over multiple stages. We study the statistical learning of optimal dynamic treatment regimes (DTRs) that guide the optimal treatment assignment for each individual at each stage based on the individual's evolving history. We propose a doubly robust, classification-based approach to learning the optimal DTR using observational data under the assumption of sequential ignorability. This approach learns the optimal DTR through backward induction. At each step, it constructs an augmented inverse probability weighting (AIPW) estimator of the policy value function and maximizes it to learn the optimal policy for the corresponding stage. We show that the resulting DTR can achieve an optimal convergence rate of $n^{-1/2}$ for welfare regret under mild convergence conditions on estimators of the nuisance components.