We consider adaptive pool-based active learning in a Bayesian setting. We first analyze two commonly used greedy active learning criteria: the maximum entropy criterion, which selects the example with the highest entropy, and the least confidence criterion, which selects the example whose most probable label has the least probability value. We show that unlike the non-adaptive case, the maximum entropy criterion is not able to achieve an approximation that is within a constant factor of optimal policy entropy. For the least confidence criterion, we show that it is able to achieve a constant factor approximation to the optimal version space reduction in a worst-case setting, where the probability of labelings that have not been eliminated is considered as the version space. We consider a third greedy active learning criterion, the Gibbs error criterion, and generalize it to handle arbitrary loss functions between labelings. We analyze the properties of the generalization and its variants, and show that they perform well in practice.
