Stochastic Proximal Algorithms with SON Regularization: Towards Efficient Optimal Transport for Domain Adaptation.

We propose a new regularizer for optimal transport (OT) which is tailored to better preserve the class structure of the subjected process. Accordingly, we provide the first theoretical guarantees for an OT scheme that respects class structure. We derive an accelerated proximal algorithm with a closed form projection and proximal operator scheme thereby affording a highly scalable algorithm for computing optimal transport plans. We provide a novel argument for the uniqueness of the optimum even in the absence of strong convexity.Our experiments show that the new regularizer does not only result in a better preservation of the class structure but also in additional robustness relative to previous regularizers.