A framework for Multi-A(rmed)/B(andit) testing with online FDR control
This addresses the need for efficient and reliable testing in applications like pharmaceutical trials and web experiments, though it is incremental by building on existing MAB and FDR methods.
The paper tackles the problem of controlling false alarms in multiple A/B tests over time by replacing them with multi-armed bandit (MAB) instances and integrating online false discovery rate (FDR) control, achieving low sample complexity and anytime FDR control as verified through simulations and real data.
We propose an alternative framework to existing setups for controlling false alarms when multiple A/B tests are run over time. This setup arises in many practical applications, e.g. when pharmaceutical companies test new treatment options against control pills for different diseases, or when internet companies test their default webpages versus various alternatives over time. Our framework proposes to replace a sequence of A/B tests by a sequence of best-arm MAB instances, which can be continuously monitored by the data scientist. When interleaving the MAB tests with an an online false discovery rate (FDR) algorithm, we can obtain the best of both worlds: low sample complexity and any time online FDR control. Our main contributions are: (i) to propose reasonable definitions of a null hypothesis for MAB instances; (ii) to demonstrate how one can derive an always-valid sequential p-value that allows continuous monitoring of each MAB test; and (iii) to show that using rejection thresholds of online-FDR algorithms as the confidence levels for the MAB algorithms results in both sample-optimality, high power and low FDR at any point in time. We run extensive simulations to verify our claims, and also report results on real data collected from the New Yorker Cartoon Caption contest.