Doubly Regularized Entropic Wasserstein Barycenters

Understand

We study a general formulation of regularized Wasserstein barycenters that enjoys favorable regularity, approximation, stability and (grid-free) optimization properties.

• This barycenter is defined as the unique probability measure that minimizes the sum of entropic optimal transport (EOT) costs with respect to a family of given probability measures, plus an entropy term.
• We denote it $(\lambda,\tau)$-barycenter, where $\lambda$ is the inner regularization strength and $\tau$ the outer one.
• This formulation recovers several previously proposed EOT barycenters for various choices of $\lambda,\tau \geq 0$ and generalizes them.