# Design Stability in Adaptive Experiments: Implications for Treatment Effect Estimation

arXiv: https://arxiv.org/abs/2510.22351 · HTML: https://mlsanity.com/paper/2510.22351/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 40 references that are in the map.
- First posted on arXiv 25 Oct 2025.

## Builds on (most cited first, 5 of 5)

- [Dynamic Causal Effects Evaluation in A/B Testing with a Reinforcement Learning Framework](https://mlsanity.com/paper/2002.01711/) (2020)
- [Efficient Adaptive Experimental Design for Average Treatment Effect Estimation](https://mlsanity.com/paper/2002.05308/) (2020)
- [Semiparametric Efficient Inference in Adaptive Experiments](https://mlsanity.com/paper/2311.18274/) (2023)
- [A randomization-based perspective of analysis of variance: a test statistic robust to treatment effect heterogeneity](https://mlsanity.com/paper/1608.01787/) (2016)
- [On mitigating the analytical limitations of finely stratified experiments](https://mlsanity.com/paper/1706.06469/) (2017)

## Built on by (most cited first, 1 of 1)

- [Fixed-Horizon Self-Normalized Inference for Adaptive Experiments via Martingale AIPW/DML with Logged Propensities](https://mlsanity.com/paper/2602.15559/) (2026)

## Abstract (arXiv)

We study the problem of estimating the average treatment effect (ATE) under sequentially adaptive treatment assignment mechanisms. In contrast to classical completely randomized designs, we consider a setting in which the probability of assigning treatment to each experimental unit may depend on prior assignments and observed outcomes. Within the potential outcomes framework, we propose and analyze two natural estimators for the ATE: the inverse propensity weighted (IPW) estimator and an augmented IPW (AIPW) estimator. The cornerstone of our analysis is the concept of design stability, which requires that as the number of units grows, either the assignment probabilities converge, or sample averages of the inverse propensity scores and of the inverse complement propensity scores converge in probability to fixed, non-random limits. Our main results establish central limit theorems for both the IPW and AIPW estimators under design stability and provide explicit expressions for their asymptotic variances. We further propose estimators for these variances, enabling the construction of asymptotically valid confidence intervals. Finally, we illustrate our theoretical results in the context of Wei's adaptive coin design and Efron's biased coin design, highlighting the applicability of the proposed methods to sequential experimentation with adaptive randomization.