# Asymptotic Inference for Multi-Stage Stationary Treatment Policy with Variable Selection

arXiv: https://arxiv.org/abs/2301.12553 · HTML: https://mlsanity.com/paper/2301.12553/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 50 references that are in the map.
- First posted on arXiv 29 Jan 2023.

## Builds on (most cited first, 17 of 17)

- [Doubly Robust Off-policy Value Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1511.03722/) (2015)
- [Data-Efficient Off-Policy Policy Evaluation for Reinforcement Learning](https://mlsanity.com/paper/1604.00923/) (2016)
- [Breaking the Curse of Horizon: Infinite-Horizon Off-Policy Estimation](https://mlsanity.com/paper/1810.12429/) (2018)
- [Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes](https://mlsanity.com/paper/1908.08526/) (2019)
- [Efficiently Breaking the Curse of Horizon in Off-Policy Evaluation with Double Reinforcement Learning](https://mlsanity.com/paper/1909.05850/) (2019)
- [Batch Policy Learning in Average Reward Markov Decision Processes](https://mlsanity.com/paper/2007.11771/) (2020)
- [Estimating Dynamic Treatment Regimes in Mobile Health Using V-learning](https://mlsanity.com/paper/1611.03531/) (2016)
- [Statistical Inference of the Value Function for Reinforcement Learning in Infinite Horizon Settings](https://mlsanity.com/paper/2001.04515/) (2020)
- [Learning When-to-Treat Policies](https://mlsanity.com/paper/1905.09751/) (2019)
- [Off-Policy Estimation of Long-Term Average Outcomes with Applications to Mobile Health](https://mlsanity.com/paper/1912.13088/) (2019)
- [Deeply-Debiased Off-Policy Interval Estimation](https://mlsanity.com/paper/2105.04646/) (2021)
- [Does the Markov Decision Process Fit the Data: Testing for the Markov Property in Sequential Decision Making](https://mlsanity.com/paper/2002.01751/) (2020)
- [Assessing Time-Varying Causal Effect Moderation in Mobile Health](https://mlsanity.com/paper/1601.00237/) (2016)
- [A General Theory of Hypothesis Tests and Confidence Regions for Sparse High Dimensional Models](https://mlsanity.com/paper/1412.8765/) (2014)
- [Off-Policy Evaluation in Partially Observed Markov Decision Processes under Sequential Ignorability](https://mlsanity.com/paper/2110.12343/) (2021)
- [Black-box Importance Sampling](https://mlsanity.com/paper/1610.05247/) (2016)
- [Estimation and inference on high-dimensional individualized treatment rule in observational data using split-and-pooled de-correlated score](https://mlsanity.com/paper/2007.04445/) (2020)

## Abstract (arXiv)

Dynamic treatment regimes or policies are a sequence of decision functions over multiple stages that are tailored to individual features. One important class of treatment policies in practice, namely multi-stage stationary treatment policies, prescribes treatment assignment probabilities using the same decision function across stages, where the decision is based on the same set of features consisting of time-evolving variables (e.g., routinely collected disease biomarkers). Although there has been extensive literature on constructing valid inference for the value function associated with dynamic treatment policies, little work has focused on the policies themselves, especially in the presence of high-dimensional feature variables. We aim to fill the gap in this work. Specifically, we first estimate the multi-stage stationary treatment policy using an augmented inverse probability weighted estimator for the value function to increase asymptotic efficiency, and further apply a penalty to select important feature variables. We then construct one-step improvements of the policy parameter estimators for valid inference. Theoretically, we show that the improved estimators are asymptotically normal, even if nuisance parameters are estimated at a slow convergence rate and the dimension of the feature variables increases with the sample size. Our numerical studies demonstrate that the proposed method estimates a sparse policy with a near-optimal value function and conducts valid inference for the policy parameters.