  The goal of the paper is to design active learning strategies which lead to
domain adaptation under an assumption of domain shift in the case of Lipschitz
labeling function. 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. Practical algorithms are inferred from
the theoretical bounds, one is based on greedy optimization and the other is a
K-medoids algorithm. We also provide improved versions of the algorithms to
address the case of large data sets. These algorithms are competitive against
other state-of-the-art active learning techniques in the context of domain
adaptation as shown in our numerical experiments, in particular on large data
sets of around one hundred thousand images.
