# Semiparametric Efficient Inference in Adaptive Experiments

arXiv: https://arxiv.org/abs/2311.18274 · HTML: https://mlsanity.com/paper/2311.18274/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 24 references that are in the map.
- First posted on arXiv 30 Nov 2023.

## Builds on (most cited first, 12 of 12)

- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Confidence Intervals for Policy Evaluation in Adaptive Experiments](https://mlsanity.com/paper/1911.02768/) (2019)
- [Statistical Inference with M-Estimators on Adaptively Collected Data](https://mlsanity.com/paper/2104.14074/) (2021)
- [Anytime-valid off-policy inference for contextual bandits](https://mlsanity.com/paper/2210.10768/) (2022)
- [Time-uniform central limit theory and asymptotic confidence sequences](https://mlsanity.com/paper/2103.06476/) (2021)
- [Efficient Adaptive Experimental Design for Average Treatment Effect Estimation](https://mlsanity.com/paper/2002.05308/) (2020)
- [Sequential Nonparametric Testing with the Law of the Iterated Logarithm](https://mlsanity.com/paper/1506.03486/) (2015)
- [Clip-OGD: An Experimental Design for Adaptive Neyman Allocation in Sequential Experiments](https://mlsanity.com/paper/2305.17187/) (2023)
- [On the near-optimality of betting confidence sets for bounded means](https://mlsanity.com/paper/2310.01547/) (2023)
- [Asymptotic Efficiency Bounds for a Class of Experimental Designs](https://mlsanity.com/paper/2205.02726/) (2022)

## Built on by (most cited first, 23 of 23)

- [Active Statistical Inference](https://mlsanity.com/paper/2403.03208/) (2024)
- [Active, anytime-valid risk controlling prediction sets](https://mlsanity.com/paper/2406.10490/) (2024)
- [Active Adaptive Experimental Design for Treatment Effect Estimation with Covariate Choices](https://mlsanity.com/paper/2403.03589/) (2024)
- [Logarithmic Neyman Regret for Adaptive Estimation of the Average Treatment Effect](https://mlsanity.com/paper/2411.14341/) (2024)
- [Adaptive Off-Policy Inference for M-Estimators Under Model Misspecification](https://mlsanity.com/paper/2509.14218/) (2025)
- [Efficient Sequential Evaluation of Large Language Models](https://mlsanity.com/paper/2607.17409/) (2026)
- [Off-policy estimation with adaptively collected data: the power of online learning](https://mlsanity.com/paper/2411.12786/) (2024)
- [Adaptive Experimental Design for Policy Learning](https://mlsanity.com/paper/2401.03756/) (2024)
- [Optimistic Algorithms for Adaptive Estimation of the Average Treatment Effect](https://mlsanity.com/paper/2502.04673/) (2025)
- [Efficient Adaptive Experimentation with Noncompliance](https://mlsanity.com/paper/2505.17468/) (2025)
- [Causal-EPIG: A Prediction-Oriented Active Learning Framework for CATE Estimation](https://mlsanity.com/paper/2509.21866/) (2025)
- [Generalized Neyman Allocation for Locally Minimax Optimal Best-Arm Identification](https://mlsanity.com/paper/2405.19317/) (2024)
- [Multi-Metric Adaptive Experimental Design Under a Fixed Budget with Validation](https://mlsanity.com/paper/2506.03062/) (2025)
- [Design Stability in Adaptive Experiments: Implications for Treatment Effect Estimation](https://mlsanity.com/paper/2510.22351/) (2025)
- [Observationally Informed Adaptive Causal Experimental Design](https://mlsanity.com/paper/2603.03785/) (2026)
- [Online Data Collection for Efficient Semiparametric Inference](https://mlsanity.com/paper/2411.03195/) (2024)
- [On Pareto Optimality for Parametric Choice Bandits](https://mlsanity.com/paper/2501.19277/) (2025)
- [Minimax and Bayes Optimal Adaptive Experimental Design for Treatment Choice](https://mlsanity.com/paper/2512.08513/) (2025)
- [Fixed-Horizon Self-Normalized Inference for Adaptive Experiments via Martingale AIPW/DML with Logged Propensities](https://mlsanity.com/paper/2602.15559/) (2026)
- [What Do We Care About in Bandits with Noncompliance? BRACE: Bandits with Recommendations, Abstention, and Certified Effects](https://mlsanity.com/paper/2603.09532/) (2026)
- [Adaptive Experimentation for Censored Survival Outcomes](https://mlsanity.com/paper/2605.18459/) (2026)
- [Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation](https://mlsanity.com/paper/2606.31184/) (2026)
- [Search Shapes Conclusions: Auditing Evidence Selection Bias in Deep Research Agents](https://mlsanity.com/paper/2609.39026/) (2026)

## Abstract (arXiv)

We consider the problem of efficient inference of the Average Treatment Effect in a sequential experiment where the policy governing the assignment of subjects to treatment or control can change over time. We first provide a central limit theorem for the Adaptive Augmented Inverse-Probability Weighted estimator, which is semiparametric efficient, under weaker assumptions than those previously made in the literature. This central limit theorem enables efficient inference at fixed sample sizes. We then consider a sequential inference setting, deriving both asymptotic and nonasymptotic confidence sequences that are considerably tighter than previous methods. These anytime-valid methods enable inference under data-dependent stopping times (sample sizes). Additionally, we use propensity score truncation techniques from the recent off-policy estimation literature to reduce the finite sample variance of our estimator without affecting the asymptotic variance. Empirical results demonstrate that our methods yield narrower confidence sequences than those previously developed in the literature while maintaining time-uniform error control.