Fast Rates in Pool-Based Batch Active Learning
Claudio Gentile, Zhilei Wang, Tong Zhang
TL;DR
<p>The paper studies pool-based batch active learning where labels are acquired in batches to reduce interaction rounds. It develops a stagewise greedy algorithm that balances informativeness and diversity through a design-inspired selection mechanism, achieving minimax-like excess-risk rates with respect to the total number of queried labels and a logarithmic number of retraining rounds. The authors extend the framework beyond linear models to logistic and general nonlinear function classes by introducing a data-dependent diversity/Dimension measure that captures model complexity and adaptivity, deriving high-probability bounds that mirror sequential minimax rates up to log factors. The results demonstrate that batch-active learning can closely match the performance of fully sequential approaches while offering practical benefits in labeling efficiency and scalability, with automatic adaptation to noise levels and mild batch-size effects.
Abstract
We consider a batch active learning scenario where the learner 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). However, batch active learning typically pays the price of a reduced adaptivity, leading to suboptimal results. In this paper we propose 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 ({\em pool-based} active learning). We analyze a novel 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 standard statistical learning settings. Our results also exhibit a mild dependence on the batch size. These are the first theoretical results that employ careful trade offs between informativeness and diversity to rigorously quantify the statistical performance of batch active learning in the pool-based scenario.