GT Transport optimal - EDP - Machine learning
Homogeneous Unbalanced Regularized Optimal Transport
March 2023
Intervenant : Théo Lacombe
Institution : Université Gustave Eiffel
Heure : 14h00 - 15h00
Lieu : 3L15

The usual (balanced) optimal transportation problem between probability measures is obviously homogeneous with respect to the mass of the measure. Given that it defines interpolations between the source and target measures, this is a natural property to expect: measuring the mass of something in grams or kilograms should not change the strategy used to transport it. However, when introducing the celebrated entropic regularization term, some inhomogeneity seemingly appears in the problem formulation. We will prove that while this phenomenon actually has no impact for balanced optimal transport (the problem surprisingly stays homogeneous), we will show that the problem becomes truly inhomogeneous when considering (regularized) unbalanced formulations of optimal transport. We will introduce a new unbalanced regularized OT model which retrieves homogeneity in general and showcase its use in the context of optimal transportation with boundary. 

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