Admissibility of Completely Randomized Trials: A Large-Deviation Approach

TL;DR

This paper demonstrates that, in multi-arm experiments, adaptive designs can universally outperform non-adaptive randomized trials in terms of efficiency, especially when using batched arm elimination strategies, resolving a key open problem.

Contribution

It proves that adaptive designs with batched arm elimination can universally dominate non-adaptive trials in large-sample regimes for three or more treatments.

Findings

Adaptive designs outperform non-adaptive trials in large samples.

Batched arm elimination strategies are key to dominance.

Results resolve an open problem in experimental design theory.

Abstract

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].