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Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size
April 9, 2024, 4:43 a.m. | Huafu Liao, Alp\'ar R. M\'esz\'aros, Chenchen Mou, Chao Zhou
cs.LG updates on arXiv.org arxiv.org
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
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