Ranking by Lifts: A Cost-Benefit Approach to Large-Scale A/B Tests

A/B testers that conduct large-scale tests often prioritize lifts as the main outcome metric and want to be able to control costs resulting from false rejections of the null. This work develops a decision-theoretic framework for maximizing profits subject to false discovery rate (FDR) control. We build an empirical Bayes solution for the problem via a greedy knapsack approach. We derive an oracle rule based on ranking the ratio of expected lifts and the cost of wrong rejections using the local false discovery rate (lfdr) statistic. Our oracle decision rule is valid and optimal for large-scale tests. Further, we establish asymptotic validity for the data-driven procedure and demonstrate finite-sample validity in experimental studies. We also demonstrate the merit of the proposed method over other FDR control methods. Finally, we discuss an application to data collected by experiments on the Optimizely platform.