  Domain adaptation (DA) is an important and emerging field of machine learning
that tackles the problem occurring when the distributions of training (source
domain) and test (target domain) data are similar but different. Current
theoretical results show that the efficiency of DA algorithms depends on their
capacity of minimizing the divergence between source and target probability
distributions. In this paper, we provide a theoretical study on the advantages
that concepts borrowed from optimal transportation theory can bring to DA. In
particular, we show that the Wasserstein metric can be used as a divergence
measure between distributions to obtain generalization guarantees for three
different learning settings: (i) classic DA with unsupervised target data (ii)
DA combining source and target labeled data, (iii) multiple source DA. Based on
the obtained results, we provide some insights showing when this analysis can
be tighter than other existing frameworks.
