2025/05/05 by Anming Gu, Juno Kim, Gu, Anming +1 · 1 citation
Computer Science · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mechanical and Optical Resonators #Optimization and Control (math.OC) #Quantum Information and Cryptography
paper · pdf · doi:10.48550/arxiv.2505.02621
openalex publication_date 2025/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The mean-field Langevin dynamics (MFLD) minimizes an entropy-regularized nonlinear convex functional on the Wasserstein space over ℝd, and has gained attention recently as a model for the gradient descent dynamics of interacting particle systems such as infinite-width two-layer neural networks. However, many problems of interest have constrained domains, which are not solved by existing mean-field algorithms due to the global diffusion term. We study the optimization of probability measures constrained to a convex subset of ℝd by proposing the mirror mean-field Langevin dynamics (MMFLD), an extension of MFLD to the mirror Langevin framework. We obtain linear convergence guarantees for the continuous MMFLD via a uniform log-Sobolev inequality, and uniform-in-time propagation of chaos results for its time- and particle-discretized counterpart.