On the Robustness of Bandit Multiple Testing

Bandit multiple hypothesis testing has broad applications in biological sciences, clinical testing for drug discovery, and online A/B/n testing. The framework utilizes an adaptive sampling strategy for multiple testing which aims to maximize statistical power while ensuring anytime false discovery rate control. This paper proposes a robust approach for bandit multiple testing, allowing for (at most) $\varepsilon$ fraction of arbitrary distribution corruption, as in Huber's contamination model. Specifically, we introduce two adaptive sampling strategies designed to minimize the number of samples required to exceed a target true positive rate, while providing anytime control over the false discovery rate. We analyze the sample complexity of our proposed methods and perform numerical simulations to demonstrate their efficiency and robustness. Furthermore, we extend our methods to address scenarios where distributions have infinite variance and situations involving multiple agents collaborating on the same bandit task.