# Optimal Adaptive Experimental Design for Estimating Treatment Effect

arXiv: https://arxiv.org/abs/2410.05552 · HTML: https://mlsanity.com/paper/2410.05552/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 66 references that are in the map.
- First posted on arXiv 7 Oct 2024.

## Builds on (most cited first, 14 of 14)

- [Statistical Inference with M-Estimators on Adaptively Collected Data](https://mlsanity.com/paper/2104.14074/) (2021)
- [On the bias, risk and consistency of sample means in multi-armed bandits](https://mlsanity.com/paper/1902.00746/) (2019)
- [Smooth Contextual Bandits: Bridging the Parametric and Non-differentiable Regret Regimes](https://mlsanity.com/paper/1909.02553/) (2019)
- [Efficient Adaptive Experimental Design for Average Treatment Effect Estimation](https://mlsanity.com/paper/2002.05308/) (2020)
- [Online Multi-Armed Bandits with Adaptive Inference](https://mlsanity.com/paper/2102.13202/) (2021)
- [Markovian Interference in Experiments](https://mlsanity.com/paper/2206.02371/) (2022)
- [Near-optimal inference in adaptive linear regression](https://mlsanity.com/paper/2107.02266/) (2021)
- [Batched Thompson Sampling](https://mlsanity.com/paper/2110.00202/) (2021)
- [Clip-OGD: An Experimental Design for Adaptive Neyman Allocation in Sequential Experiments](https://mlsanity.com/paper/2305.17187/) (2023)
- [Self-Tuning Bandits over Unknown Covariate-Shifts](https://mlsanity.com/paper/2007.08584/) (2020)
- [Statistical Inference After Adaptive Sampling for Longitudinal Data](https://mlsanity.com/paper/2202.07098/) (2022)
- [Active Adaptive Experimental Design for Treatment Effect Estimation with Covariate Choices](https://mlsanity.com/paper/2403.03589/) (2024)
- [Online Bandits with (Biased) Offline Data: Adaptive Learning under Distribution Mismatch](https://mlsanity.com/paper/2405.02594/) (2024)
- [Semiparametric theory](https://mlsanity.com/paper/1709.06418/) (2017)

## Built on by (most cited first, 5 of 5)

- [Efficient Adaptive Experimentation with Noncompliance](https://mlsanity.com/paper/2505.17468/) (2025)
- [Beyond ATE: Multi-Criteria Design for A/B Testing](https://mlsanity.com/paper/2509.05864/) (2025)
- [Learning under Distributional Drift: Prequential Reproducibility as an Intrinsic Statistical Resource](https://mlsanity.com/paper/2512.13506/) (2025)
- [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)

## Abstract (arXiv)

Given n experiment subjects with potentially heterogeneous covariates and two possible treatments, namely active treatment and control, this paper addresses the fundamental question of determining the optimal accuracy in estimating the treatment effect. Furthermore, we propose an experimental design that approaches this optimal accuracy, giving a (non-asymptotic) answer to this fundamental yet still open question. The methodological contribution is listed as following. First, we establish an idealized optimal estimator with minimal variance as benchmark, and then demonstrate that adaptive experiment is necessary to achieve near-optimal estimation accuracy. Secondly, by incorporating the concept of doubly robust method into sequential experimental design, we frame the optimal estimation problem as an online bandit learning problem, bridging the two fields of statistical estimation and bandit learning. Using tools and ideas from both bandit algorithm design and adaptive statistical estimation, we propose a general low switching adaptive experiment framework, which could be a generic research paradigm for a wide range of adaptive experimental design. Through novel lower bound techniques for non-i.i.d. data, we demonstrate the optimality of our proposed experiment. Numerical result indicates that the estimation accuracy approaches optimal with as few as two or three policy updates.