Mean-field underdamped Langevin dynamics and its spacetime discretization

Qiang Fu; Ashia Wilson

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arXiv · 2312.16360

Mean-field underdamped Langevin dynamics and its spacetime discretization

Qiang Fu·Ashia Wilson

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Abstract

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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Qiang Fu, Ashia Wilson. 2023-12-26. Mean-field underdamped Langevin dynamics and its spacetime discretization. https://arxiv.org/abs/2312.16360

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