Estimation of Optimal Dynamic Treatment Assignment Rules under Policy Constraints
This work addresses sequential intervention policies for individuals, such as in healthcare or economics, but is incremental as it builds on existing dynamic treatment regime frameworks with added constraints.
The paper tackles the problem of estimating optimal dynamic treatment assignment rules under policy constraints, proposing two empirical welfare maximization methods that achieve optimal n^{-1/2} convergence rates with finite-sample regret bounds.
Many policies involve dynamics in their treatment assignments, where individuals receive sequential interventions over multiple stages. We study estimation of an optimal dynamic treatment regime that guides the optimal treatment assignment for each individual at each stage based on their history. We propose an empirical welfare maximization approach in this dynamic framework, which estimates the optimal dynamic treatment regime using data from an experimental or quasi-experimental study while satisfying exogenous constraints on policies. The paper proposes two estimation methods: one solves the treatment assignment problem sequentially through backward induction, and the other solves the entire problem simultaneously across all stages. We establish finite-sample upper bounds on worst-case average welfare regrets for these methods and show their optimal $n^{-1/2}$ convergence rates. We also modify the simultaneous estimation method to accommodate intertemporal budget/capacity constraints.