# Estimation of Optimal Dynamic Treatment Assignment Rules under Policy Constraints

arXiv: https://arxiv.org/abs/2106.05031 · HTML: https://mlsanity.com/paper/2106.05031/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 56 references that are in the map.
- First posted on arXiv 9 Jun 2021.

## Builds on (most cited first, 7 of 7)

- [Offline Multi-Action Policy Learning: Generalization and Optimization](https://mlsanity.com/paper/1810.04778/) (2018)
- [Learning When-to-Treat Policies](https://mlsanity.com/paper/1905.09751/) (2019)
- [More Efficient Policy Learning via Optimal Retargeting](https://mlsanity.com/paper/1906.08611/) (2019)
- [Interpretable Dynamic Treatment Regimes](https://mlsanity.com/paper/1606.01472/) (2016)
- [Sample Efficient Policy Search for Optimal Stopping Domains](https://mlsanity.com/paper/1702.06238/) (2017)
- [Optimal sequential treatment allocation](https://mlsanity.com/paper/1705.09952/) (2017)
- [Identification in Nonparametric Models for Dynamic Treatment Effects](https://mlsanity.com/paper/1805.09397/) (2018)

## Abstract (arXiv)

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.