On the stability of the stochastic gradient Langevin algorithm with dependent data stream

TL;DR

This paper proves that the stochastic gradient Langevin dynamics remains stable and converges to a limiting distribution over time, even when the data stream driving the process exhibits dependencies.

Contribution

It establishes convergence of stochastic gradient Langevin dynamics under dependent data streams, extending previous results to more realistic data scenarios.

Findings

Convergence to a limiting law is guaranteed under mild conditions.

Stability holds even with dependent data streams.

Theoretical proof of convergence for dependent data.

Abstract

We prove, under mild conditions, that the stochastic gradient Langevin dynamics converges to a limiting law as time tends to infinity, even in the case where the driving data sequence is dependent.