Stochastic modified equations for the asynchronous stochastic gradient descent
Machine Learning
2020-03-04 v3 Machine Learning
Abstract
We propose a stochastic modified equations (SME) for modeling the asynchronous stochastic gradient descent (ASGD) algorithms. The resulting SME of Langevin type extracts more information about the ASGD dynamics and elucidates the relationship between different types of stochastic gradient algorithms. We show the convergence of ASGD to the SME in the continuous time limit, as well as the SME's precise prediction to the trajectories of ASGD with various forcing terms. As an application of the SME, we propose an optimal mini-batching strategy for ASGD via solving the optimal control problem of the associated SME.
Cite
@article{arxiv.1805.08244,
title = {Stochastic modified equations for the asynchronous stochastic gradient descent},
author = {Jing An and Jianfeng Lu and Lexing Ying},
journal= {arXiv preprint arXiv:1805.08244},
year = {2020}
}
Comments
Final version. To appear in Information and Inference