  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.
