On the number of trials needed to distinguish similar alternatives

A/B testing is widely used to tune search and recommendation algorithms, to compare product variants as efficiently and effectively as possible, and even to study animal behavior. With ongoing investment, due to diminishing returns, the items produced by the new alternative B show smaller and smaller improvement in quality from the items produced by the current system A. By formalizing this observation, we develop closed-form analytical expressions for the sample efficiency of a number of widely used families of slate-based comparison tests. In empirical trials, these theoretical sample complexity results are shown to be predictive of real-world testing efficiency outcomes. These findings offer opportunities for both more cost-effective testing and a better analytical understanding of the problem.