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Active learning is typically used to label data, when the labeling process isexpensive. Several active learning algorithms have been theoretically proved toperform better than their passive counterpart. However, these algorithms relyon some assumptions, which themselves contain some specific parameters. Thispaper adresses the problem of adaptive active learning in a nonparametricsetting with minimal assumptions. We present a novel algorithm that is validunder more general assumptions than the previously known algorithms, and thatcan moreover adapt to the parameters used in these assumptions. This allows usto work with a larger class of distributions, thereby avoiding to excludeimportant densities like gaussians. Our algorithm achieves a minimax rate ofconvergence, and therefore performs almost as well as the best knownnon-adaptive algorithms.

Nonparametric adaptive active learning under local smoothness condition