Mean Field Optimization Problem Regularized by Fisher Information - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Mean Field Optimization Problem Regularized by Fisher Information

Résumé

Recently there is a rising interest in the research of mean field optimization, in particular because of its role in analyzing the training of neural networks. In this paper by adding the Fisher Information as the regularizer, we relate the regularized mean field optimization problem to a so-called mean field Schrodinger dynamics. We develop an energy-dissipation method to show that the marginal distributions of the mean field Schrodinger dynamics converge exponentially quickly towards the unique minimizer of the regularized optimization problem. Remarkably, the mean field Schrodinger dynamics is proved to be a gradient flow on the probability measure space with respect to the relative entropy. Finally we propose a Monte Carlo method to sample the marginal distributions of the mean field Schrodinger dynamics.

Dates et versions

hal-04853718 , version 1 (22-12-2024)

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Julien Claisse, Giovanni Conforti, Zhenjie Ren, Songbo Wang. Mean Field Optimization Problem Regularized by Fisher Information. 2024. ⟨hal-04853718⟩
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