On the Complexity of A/B Testing

Edition Number: 
27
Date: 
June, 2014
Place: 
Barcelona, Spain
PageStart: 
461
PageEnd: 
481
Abstract: 

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.

Arxiv Number: 
1405.3224
Hal Number: 
00990254