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We consider a supervised machine learning scenario called batch active learning, where a learning agent adaptively issues batches of points to a labeling oracle. Sampling labels in batches is highly desirable in practice due to the smaller number of interactive rounds with the labeling oracle (often human beings or highly expensive pre-trained models). Yet, batch active learning typically pays the price of reduced adaptivity, leading to suboptimal convergence results. We describe a solution which requires a careful trade off between the informativeness of the queried points and their diversity. We theoretically investigate batch active learning in the practically relevant scenario where the unlabeled pool of data is available beforehand (pool-based batch active learning). We analyze a stage-wise greedy algorithm and show that, as a function of the label complexity, the excess risk of this algorithm matches the known minimax rates in a standard statistical learning setting with linear function spaces. Our results also exhibit a mild dependence on the batch size. These results are then extended to hold for general function spaces with similar algorithmics, but more involved analytical tools. 

Joint with: Z. Wang and T. Zhang.