  We study pool-based active learning with abstention feedbacks, where a
labeler can abstain from labeling a queried example with some unknown
abstention rate. This is an important problem with many useful applications. We
take a Bayesian approach to the problem and develop two new greedy algorithms
that learn both the classification problem and the unknown abstention rate at
the same time. These are achieved by simply incorporating the estimated
abstention rate into the greedy criteria. We prove that both of our algorithms
have near-optimality guarantees: they respectively achieve a
${(1-\frac{1}{e})}$ constant factor approximation of the optimal expected or
worst-case value of a useful utility function. Our experiments show the
algorithms perform well in various practical scenarios.
