# Asymptotic Efficiency Bounds for a Class of Experimental Designs

arXiv: https://arxiv.org/abs/2205.02726 · HTML: https://mlsanity.com/paper/2205.02726/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2022.

## Built on by (most cited first, 8 of 8)

- [Semiparametric Efficient Inference in Adaptive Experiments](https://mlsanity.com/paper/2311.18274/) (2023)
- [Best Arm Identification with Contextual Information under a Small Gap](https://mlsanity.com/paper/2209.07330/) (2022)
- [Asymptotically Optimal Fixed-Budget Best Arm Identification with Variance-Dependent Bounds](https://mlsanity.com/paper/2302.02988/) (2023)
- [Worst-Case Optimal Multi-Armed Gaussian Best Arm Identification with a Fixed Budget](https://mlsanity.com/paper/2310.19788/) (2023)
- [Locally Optimal Fixed-Budget Best Arm Identification in Two-Armed Gaussian Bandits with Unknown Variances](https://mlsanity.com/paper/2312.12741/) (2023)
- [Adaptive Experimental Design for Policy Learning](https://mlsanity.com/paper/2401.03756/) (2024)
- [Minimax and Bayes Optimal Adaptive Experimental Design for Treatment Choice](https://mlsanity.com/paper/2512.08513/) (2025)
- [Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation](https://mlsanity.com/paper/2606.31184/) (2026)

## Abstract (arXiv)

We consider an experimental design setting in which units are assigned to treatment after being sampled sequentially from an infinite population. We derive asymptotic efficiency bounds that apply to data from any experiment that assigns treatment as a (possibly randomized) function of covariates and past outcome data, including stratification on covariates and adaptive designs. For estimating the average treatment effect of a binary treatment, our results show that no further first order asymptotic efficiency improvement is possible relative to an estimator that achieves the Hahn (1998) bound in an experimental design where the propensity score is chosen to minimize this bound. Our results also apply to settings with multiple treatments with possible constraints on treatment, as well as covariate based sampling of a single outcome.