  We describe and analyze a new algorithm for agnostically learning
kernel-based halfspaces with respect to the \emph{zero-one} loss function.
Unlike most previous formulations which rely on surrogate convex loss functions
(e.g. hinge-loss in SVM and log-loss in logistic regression), we provide finite
time/sample guarantees with respect to the more natural zero-one loss function.
The proposed algorithm can learn kernel-based halfspaces in worst-case time
$\poly(\exp(L\log(L/\epsilon)))$, for $\emph{any}$ distribution, where $L$ is a
Lipschitz constant (which can be thought of as the reciprocal of the margin),
and the learned classifier is worse than the optimal halfspace by at most
$\epsilon$. We also prove a hardness result, showing that under a certain
cryptographic assumption, no algorithm can learn kernel-based halfspaces in
time polynomial in $L$.
