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In this paper, we aim at solving a class of multiple testing problems underthe Bayesian sequential decision framework. Our motivating application comesfrom binary labeling tasks in crowdsourcing, where the requestor needs tosimultaneously decide which worker to choose to provide the label and when tostop collecting labels under a certain budget constraint. We start with thebinary hypothesis testing problem to determine the true label of a singleobject, and provide an optimal solution by casting it under the adaptivesequential probability ratio test (Ada-SPRT) framework. We characterize thestructure of the optimal solution, i.e., optimal adaptive sequential design,which minimizes the Bayes risk through log-likelihood ratio statistic. We alsodevelop a dynamic programming algorithm that can efficiently approximate theoptimal solution. For the multiple testing problem, we further propose to adoptan empirical Bayes approach for estimating class priors and show that ourmethod has an averaged loss that converges to the minimal Bayes risk under thetrue model. The experiments on both simulated and real data show the robustnessof our method and its superiority in labeling accuracy as compared to severalother recently proposed approaches.

Optimal Stopping and Worker Selection in Crowdsourcing: an Adaptive Sequential Probability Ratio Test Framework