A Smoothed Dual Approach for Variational Wasserstein Problems

Abstract : Variational problems that involve Wasserstein distances have been recently proposed to summarize and learn from probability measures. Despite being conceptually simple, such problems are computationally challenging because they involve minimizing over quantities (Wasserstein distances) that are themselves hard to compute. We show that the dual formulation of Wasserstein variational problems introduced recently by Carlier et al. (2014) can be regularized using an entropic smoothing, which leads to smooth, differentiable, convex optimization problems that are simpler to implement and numerically more stable. We illustrate the versatility of this approach by applying it to the computation of Wasserstein barycenters and gradient flows of spacial regularization functionals.
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Contributor : Gabriel Peyré <>
Submitted on : Monday, August 31, 2015 - 8:04:02 PM
Last modification on : Friday, April 19, 2019 - 1:28:12 PM

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  • HAL Id : hal-01188954, version 1
  • ARXIV : 1503.02533



Marco Cuturi, Gabriel Peyré. A Smoothed Dual Approach for Variational Wasserstein Problems. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2015. ⟨hal-01188954⟩



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