  We study pool-based active learning of half-spaces. We revisit the aggressive
approach for active learning in the realizable case, and show that it can be
made efficient and practical, while also having theoretical guarantees under
reasonable assumptions. We further show, both theoretically and experimentally,
that it can be preferable to mellow approaches. Our efficient aggressive active
learner of half-spaces has formal approximation guarantees that hold when the
pool is separable with a margin. While our analysis is focused on the
realizable setting, we show that a simple heuristic allows using the same
algorithm successfully for pools with low error as well. We further compare the
aggressive approach to the mellow approach, and prove that there are cases in
which the aggressive approach results in significantly better label complexity
compared to the mellow approach. We demonstrate experimentally that substantial
improvements in label complexity can be achieved using the aggressive approach,
for both realizable and low-error settings.
