Optimal Transport: Forward-Backward Splitting

This lecture introduces a new forward-backward splitting algorithm for solving regularized optimal transport problems, with applications in domain adaptation and generative models. The algorithm shows significant speed and performance improvements compared to existing methods. The lecture covers the formulation of optimal transport problems, the concept of regularized optimal transport, and the use of proximity operators and proximal algorithms. It also discusses constrained optimization problems and non-smooth convex optimization. The proposed algorithm is applied to continuous domain adaptation, showcasing experimental results on different datasets. The lecture concludes with a comparison between the proposed algorithm and existing methods, highlighting its effectiveness.