Stochastic Incremental Algorithms for Optimal Transport with SON Regularizer

We introduce a new regularizer for optimal transport (OT) which is tailored to better preserve the class structure. We give the first theoretical guarantees for an OT scheme that respects class structure. We give an accelerated proximal--projection scheme for this formulation with the proximal operator in closed form to give a highly scalable algorithm for computing optimal transport plans. We give a novel argument for the uniqueness of the optimum even in the absence of strong convexity. Our experiments show that the new regularizer preserves class structure better and is more robust compared to previous regularizers.