Second order models for optimal transport and cubic splines on the Wasserstein space

2018/01/12 by Jean-David Benamou, Benamou, Jean-David, Thomas Gallouët +3 · 4 citations
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #math.OC

paper · pdf · doi:10.48550/arxiv.1801.04144

arxiv created 2018/07/26 · arxiv updated 2018/07/27

Abstract

On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation. After presenting the natural extension of cubic splines to the Wasserstein space, we propose a simpler approach based on the relaxation of the variational problem on the path space. We explore two different numerical approaches, one based on multi-marginal optimal transport and entropic regularization and the other based on semi-discrete optimal transport.

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