
Capacity Constrained Entropic Optimal Transport, Sinkhorn Saturated Domain Out-Summation and Vanishing Temperature
Benamou, Jean-David; Martinet, Mélanie (2020-05), Capacity Constrained Entropic Optimal Transport, Sinkhorn Saturated Domain Out-Summation and Vanishing Temperature. https://basepub.dauphine.fr/handle/123456789/20879
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Type
Document de travail / Working paperExternal document link
https://hal.archives-ouvertes.fr/hal-02563022Date
2020-05Publisher
Cahier de recherche CEREMADE
Published in
Paris
Pages
49
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Show full item recordAuthor(s)
Benamou, Jean-DavidCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Martinet, Mélanie
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We propose a new method to reduce the computational cost of the Entropic Optimal Transport in the vanishing temperature (ε) limit. As in [Schmitzer, 2016], the method relies on a Sinkhorn continuation "ε-scaling" approach; but instead of truncating out the small values of the Kernel, we rely on the exact "out-summation" of saturated domains for a modified constrained Entropic Optimal problem. The constraint depends on an additional parameter λ. In pratice λ = ε also vanishes and the constraint disappear. Using [Berman, 2017], the convergence of the (ε, λ) continuation method based on this modified problem is established. We then show that the saturated domain can be over estimated from the previous larger (ε, λ). On the saturated zone the solution is constant and known and the domain can be "out-summed" (removed) from Sinkhorn algorithm. The computational and cost and memory foot print is shown to be almost linear thanks again to an estimate given by [Berman, 2017]. This is confirmed on 1-D numerical experiments.Subjects / Keywords
Entropic regularization; Sinkhorn Algorithm; Optimal transport; Convex optimizationRelated items
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