# Admissibility of Completely Randomized Trials: A Large-Deviation Approach

arXiv: https://arxiv.org/abs/2506.05329 · HTML: https://mlsanity.com/paper/2506.05329/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 5 Jun 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)
- [Simple Bayesian Algorithms for Best Arm Identification](https://mlsanity.com/paper/1602.08448/) (2016)
- [Confidence Intervals for Policy Evaluation in Adaptive Experiments](https://mlsanity.com/paper/1911.02768/) (2019)
- [Inference for Batched Bandits](https://mlsanity.com/paper/2002.03217/) (2020)
- [Review on Ranking and Selection: A New Perspective](https://mlsanity.com/paper/2008.00249/) (2020)
- [On the Existence of a Complexity in Fixed Budget Bandit Identification](https://mlsanity.com/paper/2303.09468/) (2023)
- [Open Problem: Optimal Best Arm Identification with Fixed Budget](https://mlsanity.com/paper/2303.00950/) (2023)
- [Best Arm Identification with Fixed Budget: A Large Deviation Perspective](https://mlsanity.com/paper/2312.12137/) (2023)
- [Optimizing Adaptive Experiments: A Unified Approach to Regret Minimization and Best-Arm Identification](https://mlsanity.com/paper/2402.10592/) (2024)
- [Adaptive Experimentation in the Presence of Exogenous Nonstationary Variation](https://mlsanity.com/paper/2202.09036/) (2022)
- [On Universally Optimal Algorithms for A/B Testing](https://mlsanity.com/paper/2308.12000/) (2023)
- [Partial Likelihood Thompson Sampling](https://mlsanity.com/paper/2203.00820/) (2022)

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

- [Fundamental Limitations of Fixed-Budget Best-Arm Identification](https://mlsanity.com/paper/2607.11635/) (2026)

## Abstract (arXiv)

When an experimenter has the option of running an adaptive trial, is it admissible to ignore this option and run a non-adaptive trial instead? We provide a negative answer to this question in the best-arm identification problem, where the experimenter aims to allocate measurement efforts judiciously to confidently deploy the most effective treatment arm. We find that, whenever there are at least three treatment arms, there exist simple adaptive designs that universally and strictly dominate non-adaptive completely randomized trials. This dominance is characterized by a notion called efficiency exponent, which quantifies a design's statistical efficiency when the experimental sample is large. Our analysis focuses on the class of batched arm elimination designs, which progressively eliminate underperforming arms at pre-specified batch intervals. We characterize simple sufficient conditions under which these designs universally and strictly dominate completely randomized trials. These results resolve the second open problem posed in Qin [2022].