Adaptivity to Noise Parameters in Nonparametric Active Learning

Abstract: 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 \textit{noise conditions}. These rates display interesting transitions -- due to the interaction between noise \textit{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 \textit{adaptive confidence sets}, resulting in strictly milder distributional requirements.