  The goal of the paper is to design active learning strategies which lead to
domain adaptation under an assumption of Lipschitz functions. Building on
previous work by Mansour et al. (2009) we adapt the concept of discrepancy
distance between source and target distributions to restrict the maximization
over the hypothesis class to a localized class of functions which are
performing accurate labeling on the source domain. We derive generalization
error bounds for such active learning strategies in terms of Rademacher average
and localized discrepancy for general loss functions which satisfy a regularity
condition. A practical K-medoids algorithm that can address the case of large
data set is inferred from the theoretical bounds. Our numerical experiments
show that the proposed algorithm is competitive against other state-of-the-art
active learning techniques in the context of domain adaptation, in particular
on large data sets of around one hundred thousand images.
