This work addresses the problem of domain adaptation on an unlabeled target dataset using knowledge from multiple labelled source datasets. Most current approaches tackle this problem by searching for an embedding that is invariant across source and target domains, which corresponds to searching for a universal classifier that works well on all domains. In this paper, we address this problem from a new perspective: instead of crushing diversity of the source distributions, we exploit it to adapt better to the target distribution. Our method, named Multi-Source Domain Adaptation via Weighted Joint Distribution Optimal Transport (MSDA-WJDOT), aims at finding simultaneously an Optimal Transport-based alignment between the source and target distributions and a re-weighting of the sources distributions. We discuss the theoretical aspects of the method and propose a conceptually simple algorithm. Numerical experiments indicate that the proposed method achieves state-of-the-art performance on simulated and real datasets
