Propagation of Chaos for Mean-Field Langevin Dynamics and its Application to Model Ensemble
This work provides an incremental improvement in theoretical understanding for researchers in optimization and machine learning, specifically in neural network training and model ensembles.
The paper tackles the problem of improving the optimization complexity analysis for mean-field Langevin dynamics (MFLD) by refining a key inequality, resulting in the removal of exponential dependence on the regularization coefficient in the particle approximation term.
Mean-field Langevin dynamics (MFLD) is an optimization method derived by taking the mean-field limit of noisy gradient descent for two-layer neural networks in the mean-field regime. Recently, the propagation of chaos (PoC) for MFLD has gained attention as it provides a quantitative characterization of the optimization complexity in terms of the number of particles and iterations. A remarkable progress by Chen et al. (2022) showed that the approximation error due to finite particles remains uniform in time and diminishes as the number of particles increases. In this paper, by refining the defective log-Sobolev inequality -- a key result from that earlier work -- under the neural network training setting, we establish an improved PoC result for MFLD, which removes the exponential dependence on the regularization coefficient from the particle approximation term of the optimization complexity. As an application, we propose a PoC-based model ensemble strategy with theoretical guarantees.