Part of Advances in Neural Information Processing Systems 37 (NeurIPS 2024) Main Conference Track
Hoang Phuc Hau Luu, Hanlin Yu, Bernardo Williams, Petrus Mikkola, Marcelo Hartmann, Kai Puolamäki, Arto Klami
We study a class of optimization problems in the Wasserstein space (the space of probability measures) where the objective function is nonconvex along generalized geodesics. Specifically, the objective exhibits some difference-of-convex structure along these geodesics. The setting also encompasses sampling problems where the logarithm of the target distribution is difference-of-convex. We derive multiple convergence insights for a novel semi Forward-Backward Euler scheme under several nonconvex (and possibly nonsmooth) regimes. Notably, the semi Forward-Backward Euler is just a slight modification of the Forward-Backward Euler whose convergence is---to our knowledge---still unknown in our very general non-geodesically-convex setting.