Adaptivity to Noise Parameters in Nonparametric Active Learning
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This work addresses various open questions in the theory of active learning for nonparametric classification. Our contributions are both statistical and algorithmic: -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. -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.
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