Admissibility of Completely Randomized Trials: A Large-Deviation Approach
This resolves an open problem in experimental design for treatment selection, showing adaptive methods are superior, which is incremental but clarifies a theoretical gap.
The paper tackles the question of whether non-adaptive trials are admissible compared to adaptive ones in best-arm identification, finding that for at least three arms, simple adaptive designs strictly dominate non-adaptive trials in statistical efficiency as measured by an efficiency exponent.
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].