# On stochastic gradient Langevin dynamics with dependent data streams: the fully non-convex case

arXiv: https://arxiv.org/abs/1905.13142 · HTML: https://mlsanity.com/paper/1905.13142/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 14 of 14)

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- [Constrained Langevin Algorithms with L-mixing External Random Variables](https://mlsanity.com/paper/2205.14192/) (2022)
- [Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2305.15988/) (2023)
- [Unadjusted Langevin algorithm for sampling a mixture of weakly smooth potentials](https://mlsanity.com/paper/2112.09311/) (2021)
- [Regime-Switching Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2509.00941/) (2025)
- [Anchored Langevin Algorithms](https://mlsanity.com/paper/2509.19455/) (2025)
- [Weak Convergence of Approximate reflection coupling and its Application to Non-convex Optimization](https://mlsanity.com/paper/2205.11970/) (2022)
- [A Dynamical System View of Langevin-Based Non-Convex Sampling](https://mlsanity.com/paper/2210.13867/) (2022)
- [On the strong stability of ergodic iterations](https://mlsanity.com/paper/2304.04657/) (2023)
- [Improved Analysis for Hessian-free High-resolution Monte Carlo Sampling](https://mlsanity.com/paper/2608.25052/) (2026)
- [Uniform Generalization Bound on Time and Inverse Temperature for Gradient Descent Algorithm and its Application to Analysis of Simulated Annealing](https://mlsanity.com/paper/2205.12959/) (2022)
- [Asynchronous Bayesian Learning over a Network](https://mlsanity.com/paper/2211.08603/) (2022)

## Abstract (arXiv)

We consider the problem of sampling from a target distribution, which is emph not necessarily logconcave, in the context of empirical risk minimization and stochastic optimization as presented in Raginsky et al. (2017). Non-asymptotic analysis results are established in the L1-Wasserstein distance for the behaviour of Stochastic Gradient Langevin Dynamics (SGLD) algorithms. We allow the estimation of gradients to be performed even in the presence of dependent data streams. Our convergence estimates are sharper and uniform in the number of iterations, in contrast to those in previous studies.