English

Stochastic modified equations and adaptive stochastic gradient algorithms

Machine Learning 2017-06-21 v3 Machine Learning

Abstract

We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together with optimal control theory to derive novel adaptive hyper-parameter adjustment policies. Our algorithms have competitive performance with the added benefit of being robust to varying models and datasets. This provides a general methodology for the analysis and design of stochastic gradient algorithms.

Keywords

Cite

@article{arxiv.1511.06251,
  title  = {Stochastic modified equations and adaptive stochastic gradient algorithms},
  author = {Qianxiao Li and Cheng Tai and Weinan E},
  journal= {arXiv preprint arXiv:1511.06251},
  year   = {2017}
}

Comments

Major changes including a proof of the weak approximation, asymptotic expansions and application-oriented adaptive algorithms

R2 v1 2026-06-22T11:49:34.057Z