An Adaptive Strategy for Active Learning with Smooth Decision Boundary

TL;DR

This paper introduces an adaptive active learning strategy for classification with smooth decision boundaries, achieving near-optimal rates in multivariate settings without prior knowledge of distributional parameters.

Contribution

It presents the first adaptive method for multivariate active learning with smooth decision boundaries, extending previous univariate results to more practical multivariate cases.

Findings

Achieves near-optimal rates in multivariate active learning

Reduces multivariate problem to univariate-adaptive strategies

Does not require prior knowledge of distributional parameters

Abstract

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.