Optimal Transport with Adaptive Regularisation
Hugues Van Assel Titouan Vayer Remi Flamary Nicolas Courty
Regularising the primal formulation of optimal transport (OT) with a strictly
convex term leads to enhanced numerical complexity and a denser transport plan.
Many formulations impose a global constraint on the transport plan, for
instance by relying on entropic regularisation. As it is more expensive to
diffuse mass for outlier points compared to central ones, this typically
results in a significant imbalance in the way mass is spread across the points.
This can be detrimental for some applications where a minimum of smoothing is
required per point. To remedy this, we introduce OT with Adaptive
RegularIsation (OTARI), a new formulation of OT that imposes constraints on the
mass going in or/and out of each point. We then showcase the benefits of this
approach for domain adaptation.