Abstract: Our recent research focuses on advancing the field of regularized mean field optimization, with the overarching goal of establishing a theoretical foundation for evaluating the effectiveness of the training of neural networks and inspiring novel training algorithms. In this presentation, we will provide a comprehensive overview of the McKean-Vlasov dynamics, which serves as gradient flows, approaching the minimizer of regularized mean field optimization. We will place particular emphasis on examining the long-time behavior and the particle approximation of such McKean-Vlasov dynamics. Besides the gradient flows, we also introduce and investigate alternative algorithms, such as our recent work on the self-interaction diffusion, to search for the optimal weights of neural networks. Each of these algorithms is ensured to have exponential convergence, and we will showcase their performances though simple numerical tests.
Bio: I am now an Associate Professor (maître de conférence, HDR)Université Paris-Dauphine, PSL. My research so far has focused on topics closely related to the theories of stochastic process and optimal control, such as Viscosity Solutions to Path-dependent Partial Differential Equations, Backward Stochastic Differential Equations, Mean-field Games, McKean-Vlasov Stochastic Differential Equations/Propagation of Chaos, Mean-field analysis on Deep Neural NetworksNumerical Solutions to Stochastic Control Problems. I got PhD degree in Applied Mathematics from Ecole Polytechnique, France.