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

arXiv: https://arxiv.org/abs/2210.02092 · HTML: https://mlsanity.com/paper/2210.02092/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 21 references that are in the map.
- First posted on arXiv 5 Oct 2022.

## Builds on (most cited first, 3 of 3)

- [Consistency and fluctuations for stochastic gradient Langevin dynamics](https://mlsanity.com/paper/1409.0578/) (2014)
- [On stochastic gradient Langevin dynamics with dependent data streams in the logconcave case](https://mlsanity.com/paper/1812.02709/) (2018)
- [Markov chains in random environment with applications in queueing theory and machine learning](https://mlsanity.com/paper/1911.04377/) (2019)

## Built on by (most cited first, 1 of 1)

- [Transition of α-mixing in Random Iterations with Applications in Queuing Theory](https://mlsanity.com/paper/2410.05056/) (2024)

## Abstract (arXiv)

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.