Many public policies and medical interventions involve dynamics in their treatment assignments, where treatments are sequentially assigned to the same individuals across multiple stages, and the effect of treatment at each stage is usually heterogeneous with respect to the history of prior treatments and associated characteristics. We study 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 history. We propose a step-wise doubly-robust approach to learn the optimal DTR using observational data under the assumption of sequential ignorability. The approach solves the sequential treatment assignment problem through backward induction, where, at each step, we combine estimators of propensity scores and action-value functions (Q-functions) to construct augmented inverse probability weighting estimators of values of policies for each stage. The approach consistently estimates the optimal DTR if either a propensity score or Q-function for each stage is consistently estimated. Furthermore, the resulting DTR can achieve the optimal convergence rate $n^{-1/2}$ of regret under mild conditions on the convergence rate for estimators of the nuisance parameters.

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