# Active Adaptive Experimental Design for Treatment Effect Estimation with Covariate Choices arXiv: https://arxiv.org/abs/2403.03589 ยท HTML: https://mlsanity.com/paper/2403.03589/ ## Key facts - Cited by 12 papers in the map (data through 14 Oct 2026). - Builds on 26 of its 82 references that are in the map. - First posted on arXiv 6 Mar 2024. ## Builds on (most cited first, 26 of 26) - [On the Complexity of Best Arm Identification in Multi-Armed Bandit Models](https://mlsanity.com/paper/1407.4443/) (2014) - [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016) - [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) - [Simple Bayesian Algorithms for Best Arm Identification](https://mlsanity.com/paper/1602.08448/) (2016) - [Multi-armed Bandit Models for the Optimal Design of Clinical Trials: Benefits and Challenges](https://mlsanity.com/paper/1507.08025/) (2015) - [Confidence Intervals for Policy Evaluation in Adaptive Experiments](https://mlsanity.com/paper/1911.02768/) (2019) - [Inference for Batched Bandits](https://mlsanity.com/paper/2002.03217/) (2020) - [Off-Policy Evaluation via Adaptive Weighting with Data from Contextual Bandits](https://mlsanity.com/paper/2106.02029/) (2021) - [Anytime-valid off-policy inference for contextual bandits](https://mlsanity.com/paper/2210.10768/) (2022) - [Pool-Based Sequential Active Learning for Regression](https://mlsanity.com/paper/1805.04735/) (2018) - [Post-Contextual-Bandit Inference](https://mlsanity.com/paper/2106.00418/) (2021) - [Off-Policy Evaluation and Learning for External Validity under a Covariate Shift](https://mlsanity.com/paper/2002.11642/) (2020) - [Semiparametric Efficient Inference in Adaptive Experiments](https://mlsanity.com/paper/2311.18274/) (2023) - [Sequential Nonparametric Testing with the Law of the Iterated Logarithm](https://mlsanity.com/paper/1506.03486/) (2015) - [On the Existence of a Complexity in Fixed Budget Bandit Identification](https://mlsanity.com/paper/2303.09468/) (2023) - [A/B/n Testing with Control in the Presence of Subpopulations](https://mlsanity.com/paper/2110.15573/) (2021) - [Clip-OGD: An Experimental Design for Adaptive Neyman Allocation in Sequential Experiments](https://mlsanity.com/paper/2305.17187/) (2023) - [Efficient Counterfactual Learning from Bandit Feedback](https://mlsanity.com/paper/1809.03084/) (2018) - [Stratification Trees for Adaptive Randomization in Randomized Controlled Trials](https://mlsanity.com/paper/1806.05127/) (2018) - [Efficient Online Estimation of Causal Effects by Deciding What to Observe](https://mlsanity.com/paper/2108.09265/) (2021) - [The Role of Contextual Information in Best Arm Identification](https://mlsanity.com/paper/2106.14077/) (2021) - [Nonparametric extensions of randomized response for private confidence sets](https://mlsanity.com/paper/2202.08728/) (2022) - [Double machine learning and design in batch adaptive experiments](https://mlsanity.com/paper/2309.15297/) (2023) - [Asymptotically Optimal Fixed-Budget Best Arm Identification with Variance-Dependent Bounds](https://mlsanity.com/paper/2302.02988/) (2023) - [Locally Optimal Fixed-Budget Best Arm Identification in Two-Armed Gaussian Bandits with Unknown Variances](https://mlsanity.com/paper/2312.12741/) (2023) ## Built on by (most cited first, 12 of 12) - [Unraveling the Interplay between Carryover Effects and Reward Autocorrelations in Switchback Experiments](https://mlsanity.com/paper/2403.17285/) (2024) - [Optimal Adaptive Experimental Design for Estimating Treatment Effect](https://mlsanity.com/paper/2410.05552/) (2024) - [Balancing Interference and Correlation in Spatial Experimental Designs: A Causal Graph Cut Approach](https://mlsanity.com/paper/2505.20130/) (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) - [ActiveCQ: Active Estimation of Causal Quantities](https://mlsanity.com/paper/2509.24293/) (2025) - [Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates for Prediction-Powered Causal Inference](https://mlsanity.com/paper/2511.08303/) (2025) - [Designing Time Series Experiments in A/B Testing with Transformer Reinforcement Learning](https://mlsanity.com/paper/2602.01853/) (2026) - [Observationally Informed Adaptive Causal Experimental Design](https://mlsanity.com/paper/2603.03785/) (2026) - [Minimax and Bayes Optimal Adaptive Experimental Design for Treatment Choice](https://mlsanity.com/paper/2512.08513/) (2025) - [Robust Sequential Experimental Design for A/B Testing](https://mlsanity.com/paper/2605.12899/) (2026) - [Adaptive Experimentation for Censored Survival Outcomes](https://mlsanity.com/paper/2605.18459/) (2026) ## Abstract (arXiv) This study designs an adaptive experiment for efficiently estimating average treatment effects (ATEs). In each round of our adaptive experiment, an experimenter sequentially samples an experimental unit, assigns a treatment, and observes the corresponding outcome immediately. At the end of the experiment, the experimenter estimates an ATE using the gathered samples. The objective is to estimate the ATE with a smaller asymptotic variance. Existing studies have designed experiments that adaptively optimize the propensity score (treatment-assignment probability). As a generalization of such an approach, we propose optimizing the covariate density as well as the propensity score. First, we derive the efficient covariate density and propensity score that minimize the semiparametric efficiency bound and find that optimizing both covariate density and propensity score minimizes the semiparametric efficiency bound more effectively than optimizing only the propensity score. Next, we design an adaptive experiment using the efficient covariate density and propensity score sequentially estimated during the experiment. Lastly, we propose an ATE estimator whose asymptotic variance aligns with the minimized semiparametric efficiency bound.