This is an online seminar. Registration is required.
【Team】Deep Learning Theory Team
【Date】2024/December/23(Mon) 17:00-18:00(JST)
【Speaker】Razvan Lascu, Heriot-Watt University
Title: Linear convergence of proximal descent schemes on the Wasserstein space
Abstract: We investigate proximal descent methods, inspired by the minimizing movement scheme introduced by Jordan, Kinderlehrer and Otto, for optimizing entropy regularized functionals on the Wasserstein space. We establish linear convergence under flat convexity assumptions, thereby relaxing the common reliance on geodesic convexity. Our analysis circumvents the need for discrete-time adaptations of the Evolution Variational Inequality (EVI). Instead, we leverage a uniform logarithmic Sobolev inequality (LSI) and the entropy “sandwich” lemma, extending the analysis from [Nitanda et al., 2022 - Convex Analysis of the Mean Field Langevin Dynamics] and [Chizat, 2022 - Mean-Field Langevin Dynamics : Exponential Convergence and Annealing] .
