  We study the learnability of linear separators in $\Re^d$ in the presence of
bounded (a.k.a Massart) noise. This is a realistic generalization of the random
classification noise model, where the adversary can flip each example $x$ with
probability $\eta(x) \leq \eta$. We provide the first polynomial time algorithm
that can learn linear separators to arbitrarily small excess error in this
noise model under the uniform distribution over the unit ball in $\Re^d$, for
some constant value of $\eta$. While widely studied in the statistical learning
theory community in the context of getting faster convergence rates,
computationally efficient algorithms in this model had remained elusive. Our
work provides the first evidence that one can indeed design algorithms
achieving arbitrarily small excess error in polynomial time under this
realistic noise model and thus opens up a new and exciting line of research.
  We additionally provide lower bounds showing that popular algorithms such as
hinge loss minimization and averaging cannot lead to arbitrarily small excess
error under Massart noise, even under the uniform distribution. Our work
instead, makes use of a margin based technique developed in the context of
active learning. As a result, our algorithm is also an active learning
algorithm with label complexity that is only a logarithmic the desired excess
error $\epsilon$.
