Activized Learning: Transforming Passive to Active with Improved Label Complexity∗ Working Notes: Updated January 2011

We study the theoretical advantages of active learning over passive learning. Specifically, we prove that, in noise-free classifier learning for VC classes, any passive learning algorithm can be transformed into an active learning algorithm with asymptotically strictly superior label complexity for all nontrivial target functions and distributions, in many cases without significant loss in computational efficiency. We further provide a general characterization of the magnitude of these improvements in terms of a novel generalization of the disagreement coefficient. We also extend these results to active learning in the presence of label noise, and find that even under broad classes of noise distributions, we can typically guarantee strict improvements over the known results for passive learning.