Light Unbalanced Optimal Transport

Understand

While the continuous Entropic Optimal Transport (EOT) field has been actively developing in recent years, it became evident that the classic EOT problem is prone to different issues like the sensitivity to outliers and imbalance of classes in the source and target measures.

• This fact inspired the development of solvers that deal with the unbalanced EOT (UEOT) problem $-$ the generalization of EOT allowing for mitigating the mentioned issues by relaxing the marginal constraints.
• Surprisingly, it turns out that the existing solvers are either based on heuristic principles or heavy-weighted with complex optimization objectives involving several neural networks.
• We address this challenge and propose a novel theoretically-justified, lightweight, unbalanced EOT solver.