# Minimax and Bayes Optimal Adaptive Experimental Design for Treatment Choice

arXiv: https://arxiv.org/abs/2512.08513 · HTML: https://mlsanity.com/paper/2512.08513/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 42 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Builds on (most cited first, 13 of 13)

- [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)
- [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)
- [Clip-OGD: An Experimental Design for Adaptive Neyman Allocation in Sequential Experiments](https://mlsanity.com/paper/2305.17187/) (2023)
- [On the Complexity of A/B Testing](https://mlsanity.com/paper/1405.3224/) (2014)
- [Active Adaptive Experimental Design for Treatment Effect Estimation with Covariate Choices](https://mlsanity.com/paper/2403.03589/) (2024)
- [Rate-optimal Bayesian Simple Regret in Best Arm Identification](https://mlsanity.com/paper/2111.09885/) (2021)
- [Asymptotic Efficiency Bounds for a Class of Experimental Designs](https://mlsanity.com/paper/2205.02726/) (2022)
- [Risk and optimal policies in bandit experiments](https://mlsanity.com/paper/2112.06363/) (2021)
- [Logarithmic Neyman Regret for Adaptive Estimation of the Average Treatment Effect](https://mlsanity.com/paper/2411.14341/) (2024)
- [Stronger Neyman Regret Guarantees for Adaptive Experimental Design](https://mlsanity.com/paper/2502.17427/) (2025)
- [Generalized Neyman Allocation for Locally Minimax Optimal Best-Arm Identification](https://mlsanity.com/paper/2405.19317/) (2024)

## Abstract (arXiv)

We consider an adaptive experiment for treatment choice and design a minimax and Bayes optimal adaptive experiment with respect to regret. Given binary treatments, the experimenter's goal is to choose the treatment with the highest expected outcome through an adaptive experiment, in order to maximize welfare. We consider adaptive experiments that consist of two phases, the treatment allocation phase and the treatment choice phase. The experiment starts with the treatment allocation phase, where the experimenter allocates treatments to experimental subjects to gather observations. During this phase, the experimenter can adaptively update the allocation probabilities using the observations obtained in the experiment. After the allocation phase, the experimenter proceeds to the treatment choice phase, where one of the treatments is selected as the best. For this adaptive experimental procedure, we propose an adaptive experiment that splits the treatment allocation phase into two stages, where we first estimate the standard deviations and then allocate each treatment proportionally to its standard deviation. We show that this experiment, often referred to as Neyman allocation, is minimax and Bayes optimal in the sense that its regret upper bounds exactly match the lower bounds that we derive. To show this optimality, we derive minimax and Bayes lower bounds for the regret using change-of-measure arguments. Then, we evaluate the corresponding upper bounds using the central limit theorem and large deviation bounds.