An Adaptive Strategy for Active Learning with Smooth Decision Boundary
This solves a long-standing open problem in active learning for multivariate data, which is more practical than univariate cases.
The paper tackles the problem of adaptive active learning for classification with smooth decision boundaries in multivariate data, achieving near-optimal rates without prior knowledge of distributional parameters.
We present the first adaptive strategy for active learning in the setting of classification with smooth decision boundary. The problem of adaptivity (to unknown distributional parameters) has remained opened since the seminal work of Castro and Nowak (2007), which first established (active learning) rates for this setting. While some recent advances on this problem establish adaptive rates in the case of univariate data, adaptivity in the more practical setting of multivariate data has so far remained elusive. Combining insights from various recent works, we show that, for the multivariate case, a careful reduction to univariate-adaptive strategies yield near-optimal rates without prior knowledge of distributional parameters.