# Adaptive Neyman Allocation

arXiv: https://arxiv.org/abs/2309.08808 · HTML: https://mlsanity.com/paper/2309.08808/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2023.

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

- [Learning treatment effects while treating those in need](https://mlsanity.com/paper/2407.07596/) (2024)
- [Prediction-Guided Active Experiments](https://mlsanity.com/paper/2411.12036/) (2024)
- [Allocation Stability and Wald Inference under Variance-Aware UCB](https://mlsanity.com/paper/2412.08843/) (2024)
- [Simulation-Based Inference for Adaptive Experiments](https://mlsanity.com/paper/2506.02881/) (2025)
- [Privacy Preserving Adaptive Experiment Design](https://mlsanity.com/paper/2401.08224/) (2024)
- [Online Data Collection for Efficient Semiparametric Inference](https://mlsanity.com/paper/2411.03195/) (2024)
- [Beyond ATE: Multi-Criteria Design for A/B Testing](https://mlsanity.com/paper/2509.05864/) (2025)
- [Optimal Sequential Annotations for Off-Policy Evaluation](https://mlsanity.com/paper/2609.26707/) (2026)

## Abstract (arXiv)

In the experimental design literature, Neyman allocation refers to the practice of allocating units into treated and control groups, potentially in unequal numbers proportional to their respective standard deviations, with the objective of minimizing the variance of the treatment effect estimator. This widely recognized approach increases statistical power in scenarios where the treated and control groups have different standard deviations, as is often the case in social experiments, clinical trials, marketing research, and online A/B testing. However, Neyman allocation cannot be implemented unless the standard deviations are known in advance. Fortunately, the multi-stage nature of the aforementioned applications allows the use of earlier stage observations to estimate the standard deviations, which further guide allocation decisions in later stages. In this paper, we introduce a competitive analysis framework to study this multi-stage experimental design problem. We propose a simple adaptive Neyman allocation algorithm, which almost matches the information-theoretic limit of conducting experiments. We provide theory for estimation and inference using data collected from our adaptive Neyman allocation algorithm. We demonstrate the effectiveness of our adaptive Neyman allocation algorithm using both online A/B testing data from a social media site and synthetic data.