Non-equilibrium kinetic SDEs under partial dissipation are shown to satisfy exponential ergodicity in relative entropy and L2-Wasserstein distance, with extensions to McKean-Vlasov and mean-field particle systems.
Mean-field underdamped Langevin dynamics and its spacetime discretization
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We propose a new method called the N-particle underdamped Langevin algorithm for optimizing a special class of non-linear functionals defined over the space of probability measures. Examples of problems with this formulation include training mean-field neural networks, maximum mean discrepancy minimization and kernel Stein discrepancy minimization. Our algorithm is based on a novel spacetime discretization of the mean-field underdamped Langevin dynamics, for which we provide a new, fast mixing guarantee. In addition, we demonstrate that our algorithm converges globally in total variation distance, bridging the theoretical gap between the dynamics and its practical implementation.
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Exponential Ergodicity in Relative Entropy and $L^2$-Wasserstein Distance for non-equilibrium partially dissipative Kinetic SDEs
Non-equilibrium kinetic SDEs under partial dissipation are shown to satisfy exponential ergodicity in relative entropy and L2-Wasserstein distance, with extensions to McKean-Vlasov and mean-field particle systems.