Convex Analysis of the Mean Field Langevin Dynamics. (arXiv:2201.10469v1 [stat.ML])

As an example of the nonlinear Fokker-Planck equation, the mean field
Langevin dynamics attracts attention due to its connection to (noisy) gradient
descent on infinitely wide neural networks in the mean field regime, and hence
the convergence property of the dynamics is of great theoretical interest. In
this work, we give a simple and self-contained convergence rate analysis of the
mean field Langevin dynamics with respect to the (regularized) objective
function in both continuous and discrete time settings. The key …

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