  We develop a computationally-efficient PAC active learning algorithm for
$d$-dimensional homogeneous halfspaces that can tolerate Massart
noise~\citep{massart2006risk} and Tsybakov noise~\citep{tsybakov2004optimal}.
Specialized to the $\eta$-Massart noise setting, our algorithm achieves an
information-theoretic optimal label complexity of $\tilde{O}\left(
\frac{d}{(1-2\eta)^2} \mathrm{polylog}(\frac1\epsilon) \right)$ under a wide
range of unlabeled data distributions (specifically, the family of "structured
distributions" defined in~\citet{diakonikolas2020polynomial}). Under the more
challenging Tsybakov noise condition, we identify two subfamilies of noise
conditions, under which our algorithm achieves computational efficiency and
provide label complexity guarantees strictly lower than passive learning
algorithms.
