On the Complexity of A/B Testing
This work addresses the complexity of A/B testing for practitioners and researchers, offering incremental improvements in theoretical bounds and practical algorithms.
The paper tackles the problem of determining the best option in A/B testing with random outcomes, providing distribution-dependent lower bounds that improve over existing results in both fixed-confidence and fixed-budget settings, including faster termination in some cases.
A/B testing refers to the task of determining the best option among two alternatives that yield random outcomes. We provide distribution-dependent lower bounds for the performance of A/B testing that improve over the results currently available both in the fixed-confidence (or delta-PAC) and fixed-budget settings. When the distribution of the outcomes are Gaussian, we prove that the complexity of the fixed-confidence and fixed-budget settings are equivalent, and that uniform sampling of both alternatives is optimal only in the case of equal variances. In the common variance case, we also provide a stopping rule that terminates faster than existing fixed-confidence algorithms. In the case of Bernoulli distributions, we show that the complexity of fixed-budget setting is smaller than that of fixed-confidence setting and that uniform sampling of both alternatives -though not optimal- is advisable in practice when combined with an appropriate stopping criterion.