Year: 2023
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Institutions: École Normale Supérieure de Lyon, Unité de Mathématiques Pures et Appliquées, Laboratoire de Physique de l'ENS de Lyon, Laboratoire de l'Informatique du Parallélisme, OCKHAM: Optimisation, Connaissances pHysiques, Algorithmes et Modèles, Centre de Mathématiques Appliquées de l'École polytechnique, Institut de Recherche en Informatique et Systèmes Aléatoires
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4387356706