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Communication Dans Un Congrès Année : 2017

Overrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport

Résumé

This article describes a method for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely-used iterative Bregman projections algorithm (or Sinkhorn-Knopp algorithm). The idea is to overrelax the Bregman projection operators, allowing for faster convergence. In practice this corresponds to elevating the diagonal scaling factors to a given power, at each step of the algorithm. We propose a simple method for establishing global convergence by ensuring the decrease of a Lyapunov function at each step. An adaptive choice of overrelaxation parameter based on the Lyapunov function is constructed. We also suggest a heuristic to choose a suitable asymptotic overrelaxation parameter, based on a local convergence analysis. Our numerical experiments show a gain in convergence speed by an order of magnitude in certain regimes.
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Dates et versions

hal-01629985 , version 1 (22-07-2019)

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Alexis Thibault, Lenaic Chizat, Charles H Dossal, Nicolas Papadakis. Overrelaxed Sinkhorn-Knopp Algorithm for Regularized Optimal Transport. NIPS Workshop on Optimal Transport & Machine Learning (OTML'17), Dec 2017, Long Beach, United States. ⟨hal-01629985⟩
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