May 9 – 11, 2023
Dijon (campus de l'U. Bourgogne)
Europe/Paris timezone

Convergence rate of general entropic optimal transport costs

May 10, 2023, 9:00 AM
45m
Salle René Baire (4th floor) (Dijon (campus de l'U. Bourgogne))

Salle René Baire (4th floor)

Dijon (campus de l'U. Bourgogne)

Faculté des Sciences Mirande 9 avenue Alain Savary - 21078 Dijon Cedex

Speaker

Guillaume Carlier

Description

In recent years, the entropic approximation of the optimal transport problem has received a lot of attention because of its connection with the popular Sinkhorn scaling algorithm. In this talk, I will give a sharp convergence rate of convergence for the value of the entropic 
cost to the optimal transport cost as the entropic parameter becomes small. The class of transport costs considered is quite general and covers situations where there is no Monge solution. Upper bounds will be obtained by a block approximation strategy and a refinement of Alexandrov’s theorem. The (matching) lower bound will be obtained, under a nondegeneracy condition, by a quadratic detachment bound derived from Minty’s trick. This is a joint work with Paul Pegon and Luca Tamanini.

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