  Active learning is an important technique to reduce the number of labeled
examples in supervised learning. Active learning for binary classification has
been well addressed in machine learning. However, active learning of the reject
option classifier remains unaddressed. In this paper, we propose novel
algorithms for active learning of reject option classifiers. We develop an
active learning algorithm using double ramp loss function. We provide mistake
bounds for this algorithm. We also propose a new loss function called double
sigmoid loss function for reject option and corresponding active learning
algorithm. We offer a convergence guarantee for this algorithm. We provide
extensive experimental results to show the effectiveness of the proposed
algorithms. The proposed algorithms efficiently reduce the number of label
examples required.
