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Contextual bandit algorithms are increasingly replacing non-adaptive A/B tests in e-commerce, healthcare, and policymaking because they can both improve outcomes for study participants and increase the chance of identifying good or even best policies. To support credible inference on novel interventions at the end of the study, nonetheless, we still want to construct valid confidence intervals on average treatment effects, subgroup effects, or value of new policies. The adaptive nature of the data collected by contextual bandit algorithms, however, makes this difficult: standard estimators are no longer asymptotically normally distributed and classic confidence intervals fail to provide correct coverage. While this has been addressed in non-contextual settings by using stabilized estimators, variance stabilized estimators in the contextual setting pose unique challenges that we tackle for the first time in this paper. We propose the Contextual Adaptive Doubly Robust (CADR) estimator, a novel estimator for policy value that is asymptotically normal under contextual adaptive data collection. The main technical challenge in constructing CADR is designing adaptive and consistent conditional standard deviation estimators for stabilization. Extensive numerical experiments using 57 OpenML datasets demonstrate that confidence intervals based on CADR uniquely provide correct coverage.
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This content will become publicly available on August 25, 2026
Asymptotic Inference for Multi-Stage Stationary Treatment Policy with Variable Selection
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 obtain the multi-stage stationary treatment policy by minimizing the negative augmented inverse probability weighted estimator of the value function to increase asymptotic efficiency. A penalty is applied on the policy parameters 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.
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- Award ID(s):
- 2100729
- PAR ID:
- 10630411
- Editor(s):
- zhu, Ji
- Publisher / Repository:
- Journal of Machine Learning Research
- Date Published:
- Journal Name:
- Journal of machine learning
- ISSN:
- 2790-203X
- Subject(s) / Keyword(s):
- Augmented inverse probability weighted estimator, dynamic treatment regime, high-dimensional inference, policy parameter, sparse estimation
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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