Adaptivity to Noise Parameters in Nonparametric Active Learning


Carpentier Alexandra Locatelli Andrea, Kpotufe Samory ;
Proceedings of the 2017 Conference on Learning Theory, PMLR 65:1383-1416, 2017.


This work addresses various open questions in the theory of active learning for nonparametric classification. Our contributions are both statistical and algorithmic: \beginitemize \item We establish new minimax-rates for active learning under common noise conditions. These rates display interesting transitions – due to the interaction between noise smoothness and margin – not present in the passive setting. Some such transitions were previously conjectured, but remained unconfirmed. \item We present a generic algorithmic strategy for adaptivity to unknown noise smoothness and margin; our strategy achieves optimal rates in many general situations; furthermore, unlike in previous work, we avoid the need for adaptive confidence sets, resulting in strictly milder distributional requirements. \enditemize

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