A1297
Title: Entropic optimal transport beyond product reference couplings: The Gaussian case on Euclidean space
Authors: Nikitas Georgakis - EPFL (Switzerland) [presenting]
Abstract: Optimal transport (OT) provides a framework for comparing probability measures by minimizing the cost of transporting mass from one distribution to another. Since its formulation by Kantorovich, OT has found applications in mathematics, economics, physics, imaging, and machine learning. Despite its theoretical elegance, the classical OT problem faces significant challenges. Regularizing the OT problem with an entropy term yields an approximation known as entropic optimal transport. Entropic penalties steer the induced coupling toward a reference measure with desired properties. The use of product measure as the reference has been thoroughly studied. The case where the reference coupling is not a product is considered, focusing on the Gaussian setting as a core paradigm. It is shown that such a regularized OT problem can be reduced to a matrix optimization problem, which allows for a complete characterization of the solution in both primal and dual terms. Beyond its intrinsic interest, allowing non-product references is essential in dynamic statistical settings. As a key motivation, the reconstruction of trajectory dynamics from finitely many time marginals is studied. Unlike product references, Gaussian process references yield transitions that assemble into a coherent continuous time process.
