A Bandit Approach to Sequential Experimental Design with False Discovery Control

We propose a new adaptive sampling approach to multiple testing which aims to maximize statistical power while ensuring anytime false discovery control. We consider $n$ distributions whose means are partitioned by whether they are below or equal to a baseline (nulls), versus above the baseline (true positives). In addition, each distribution can be sequentially and repeatedly sampled. Using techniques from multi-armed bandits, we provide an algorithm that takes as few samples as possible to exceed a target true positive proportion (i.e. Our sample complexity results match known information theoretic lower bounds and through simulations we show a substantial performance improvement over uniform sampling and an adaptive elimination style algorithm.