In many scientific settings there is a need for adaptive experimental design\nto guide the process of identifying regions of the search space that contain as\nmany true positives as possible subject to a low rate of false discoveries\n(i.e. false alarms). Such regions of the search space could differ drastically\nfrom a predicted set that minimizes 0/1 error and accurate identification could\nrequire very different sampling strategies. Like active learning for binary\nclassification, this experimental design cannot be optimally chosen a priori,\nbut rather the data must be taken sequentially and adaptively. However, unlike\nclassification with 0/1 error, collecting data adaptively to find a set with\nhigh true positive rate and low false discovery rate (FDR) is not as well\nunderstood. In this paper we provide the first provably sample efficient\nadaptive algorithm for this problem. Along the way we highlight connections\nbetween classification, combinatorial bandits, and FDR control making\ncontributions to each.\n