Theoretical Analysis of Domain Adaptation with Optimal Transport

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. We also show that in the context of multiple source DA, the problem of estimating of the best joint hypothesis between source and target labeling functions can be reformulated using a Wasserstein distance-based loss function. We think that these results open the door to novel ideas and directions for DA.