Functional Central Limit Theorem and Strong Law of Large Numbers for Stochastic Gradient Langevin Dynamics

被引：0
作者：
A. Lovas
M. Rásonyi
机构：
[1] Alfréd Rényi Institute of Mathematics: Renyi Alfred Matematikai Kutatointezet,
[2] Budapest University of Technology and Economics: Budapesti Műszaki és Gazdaságtudományi Egyetem,undefined
[3] Eotvos Lorand University: Eötvös Loránd Tudományegyetem,undefined
来源：
Applied Mathematics & Optimization | 2023年 / 88卷
关键词：
Stochastic gradient descent; Online learning; Functional central limit theorem; Mixing; Markov chains in random environments;
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摘要：
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 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.
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