Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size

arXiv:2404.05185v1 Announce Type: cross
Abstract: This paper deals with a class of neural SDEs and studies the limiting behavior of the associated sampled optimal control problems as the sample size grows to infinity. The neural SDEs with N samples can be linked to the N-particle systems with centralized control. We analyze the Hamilton--Jacobi--Bellman equation corresponding to the N-particle system and establish regularity results which are uniform in N. The uniform regularity estimates are obtained by the stochastic maximum principle and …

abstract analysis arxiv behavior class control convergence cs.lg deals deep learning math.oc math.pr paper particle sample samples stat.ml studies systems type