This paper studies statistical decisions for dynamic treatment assignment
problems. Many policies involve dynamics in their treatment assignments where
treatments are sequentially assigned to individuals across multiple stages and
the effect of treatment at each stage is usually heterogeneous with respect to
the prior treatments, past outcomes, and observed covariates. We consider
estimating an optimal dynamic treatment rule that guides the optimal treatment
assignment for each individual at each stage based on the individual's history.
This paper proposes an empirical welfare maximization approach in a dynamic
framework. The approach estimates the optimal dynamic treatment rule from panel
data taken from an experimental or quasi-experimental study. The paper proposes
two estimation methods: one solves the treatment assignment problem at each
stage through backward induction, and the other solves the whole dynamic
treatment assignment problem simultaneously across all stages. We derive
finite-sample upper bounds on the worst-case average welfare-regrets for the
proposed methods and show $n^{-1/2}$-minimax convergence rates. We also modify
the simultaneous estimation method to incorporate intertemporal budget/capacity
constraints.