Sampling From the Wasserstein Barycenter
This work addresses a computational challenge in optimal transport for researchers and practitioners, but it appears incremental as it builds on existing formulations with a penalization approach.
The authors tackled the problem of sampling from the Wasserstein barycenter of absolutely continuous measures by developing an algorithm based on a penalized multimarginal gradient flow, proving that the coupling approximates the barycenter and demonstrating its performance in various settings.
This work presents an algorithm to sample from the Wasserstein barycenter of absolutely continuous measures. Our method is based on the gradient flow of the multimarginal formulation of the Wasserstein barycenter, with an additive penalization to account for the marginal constraints. We prove that the minimum of this penalized multimarginal formulation is achieved for a coupling that is close to the Wasserstein barycenter. The performances of the algorithm are showcased in several settings.