Uniform-in-Time Propagation of Chaos for Mean Field Langevin Dynamics

Fan Chen , Zhenjie Ren (1) , Songbo Wang

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We study the uniform-in-time propagation of chaos for mean field Langevin dynamics with convex mean field potenital. Convergences in both Wasserstein-$2$ distance and relative entropy are established. We do not require the mean field potenital functional to bear either small mean field interaction or displacement convexity, which are common constraints in the literature. In particular, it allows us to study the efficiency of the noisy gradient descent algorithm for training two-layer neural networks.

Domaines: Equations aux dérivées partielles [math.AP]; Apprentissage [cs.LG]; Optimisation et contrôle [math.OC]

Fan Chen, Zhenjie Ren, Songbo Wang. Uniform-in-Time Propagation of Chaos for Mean Field Langevin Dynamics. 2022. ⟨hal-03909136⟩