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We introduce in this paper a novel strategy for efficiently approximating theSinkhorn distance between two discrete measures. After identifying neglectablecomponents of the dual solution of the regularized Sinkhorn problem, we proposeto screen those components by directly setting them at that value beforeentering the Sinkhorn problem. This allows us to solve a smaller Sinkhornproblem while ensuring approximation with provable guarantees. More formally,the approach is based on a new formulation of dual of Sinkhorn divergenceproblem and on the KKT optimality conditions of this problem, which enableidentification of dual components to be screened. This new analysis leads tothe Screenkhorn algorithm. We illustrate the efficiency of Screenkhorn oncomplex tasks such as dimensionality reduction and domain adaptation involvingregularized optimal transport.

Screening Sinkhorn Algorithm for Regularized Optimal Transport