Functional Central Limit Theorem and Strong Law of Large Numbers for Stochastic Gradient Langevin Dynamics
Probability
2023-08-01 v2 Machine Learning
Optimization and Control
Abstract
We study the mixing properties of an important optimization algorithm of machine learning: the stochastic gradient Langevin dynamics (SGLD) with a fixed step size. The data stream is not assumed to be independent hence the SGLD is not a Markov chain, merely a \emph{Markov chain in a random environment}, which complicates the mathematical treatment considerably. We derive a strong law of large numbers and a functional central limit theorem for SGLD.
Keywords
Cite
@article{arxiv.2210.02092,
title = {Functional Central Limit Theorem and Strong Law of Large Numbers for Stochastic Gradient Langevin Dynamics},
author = {Attila Lovas and Miklós Rásonyi},
journal= {arXiv preprint arXiv:2210.02092},
year = {2023}
}
Comments
16 pages