Mean-field underdamped Langevin dynamics and its spacetime discretization

• URL: http://arxiv.org/abs/2312.16360v5
• Date: Tue, 6 Feb 2024 06:06:09 GMT
• Title: Mean-field underdamped Langevin dynamics and its spacetime discretization
• Authors: Qiang Fu, Ashia Wilson
• Abstract summary: 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. Our algorithm is based on a novel spacetime discretization of the mean-field underdamped Langevin dynamics.
• Score: 5.832709207282124
• License: http://creativecommons.org/licenses/by/4.0/
• 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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