In many scientific settings there is a need for adaptive experimental design to guide the process of identifying regions of the search space that contain as many true positives as possible subject to a low rate of false discoveries (i.e.

Originality: The problem considered in this paper has not been extensively studied yet. The proposed solution is based on a nice combination of techniques from active learning and combinatorial bandits. Quality: I didn't check proofs in appendix, but results look reasonable to me. Clarity: This paper is well-organized. However, its technical part is a little bit dense and more explanation might be helpful.

In many scientific settings there is a need for adaptive experimental design to guide the process of identifying regions of the search space that contain as many true positives as possible subject to a low rate of false discoveries (i.e. Such regions of the search space could differ drastically from a predicted set that minimizes 0/1 error and accurate identification could require very different sampling strategies. Like active learning for binary classification, this experimental design cannot be optimally chosen a priori, but rather the data must be taken sequentially and adaptively in a closed loop. However, unlike classification with 0/1 error, collecting data adaptively to find a set with high true positive rate and low false discovery rate (FDR) is not as well understood. In this paper, we provide the first provably sample efficient adaptive algorithm for this problem.

In many scientific settings there is a need for adaptive experimental design to guide the process of identifying regions of the search space that contain as many true positives as possible subject to a low rate of false discoveries (i.e. Such regions of the search space could differ drastically from a predicted set that minimizes 0/1 error and accurate identification could require very different sampling strategies. Like active learning for binary classification, this experimental design cannot be optimally chosen a priori, but rather the data must be taken sequentially and adaptively in a closed loop. However, unlike classification with 0/1 error, collecting data adaptively to find a set with high true positive rate and low false discovery rate (FDR) is not as well understood. In this paper, we provide the first provably sample efficient adaptive algorithm for this problem.