Adaptivity to Noise Parameters in Nonparametric Active Learning

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 $\mathit{\text{noise}}\mathit{\text{conditions}}$. These rates display interesting transitions – due to the interaction between noise $\mathit{\text{smoothness}}\mathit{\text{and}}\mathit{\text{margin}}$ – 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 $\mathit{\text{adaptive}}\mathit{\text{confidence}}\mathit{\text{sets}}$, resulting in strictly milder distributional requirements.