# Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimization

arXiv: https://arxiv.org/abs/1910.02008 · HTML: https://mlsanity.com/paper/1910.02008/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2019.

## Built on by (most cited first, 30 of 38)

- [Time-independent Generalization Bounds for SGLD in Non-convex Settings](https://mlsanity.com/paper/2111.12876/) (2021)
- [Interacting Particle Langevin Algorithm for Maximum Marginal Likelihood Estimation](https://mlsanity.com/paper/2303.13429/) (2023)
- [Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case](https://mlsanity.com/paper/2301.08039/) (2023)
- [Time-Independent Information-Theoretic Generalization Bounds for SGLD](https://mlsanity.com/paper/2311.01046/) (2023)
- [Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networks](https://mlsanity.com/paper/2105.13937/) (2021)
- [Non-asymptotic estimates for TUSLA algorithm for non-convex learning with applications to neural networks with ReLU activation function](https://mlsanity.com/paper/2107.08649/) (2021)
- [Proximal Interacting Particle Langevin Algorithms](https://mlsanity.com/paper/2406.14292/) (2024)
- [Convergence Analysis of Schr"odinger-F"ollmer Sampler without Convexity](https://mlsanity.com/paper/2107.04766/) (2021)
- [Utilising the CLT Structure in Stochastic Gradient based Sampling : Improved Analysis and Faster Algorithms](https://mlsanity.com/paper/2206.03792/) (2022)
- [Taming under isoperimetry](https://mlsanity.com/paper/2311.09003/) (2023)
- [Tamed Langevin sampling under weaker conditions](https://mlsanity.com/paper/2405.17693/) (2024)
- [Kinetic Interacting Particle Langevin Monte Carlo](https://mlsanity.com/paper/2407.05790/) (2024)
- [Langevin dynamics based algorithm e-THvarepsilonO POULA for stochastic optimization problems with discontinuous stochastic gradient](https://mlsanity.com/paper/2210.13193/) (2022)
- [From Global to Local: A Scalable Benchmark for Local Posterior Sampling](https://mlsanity.com/paper/2507.21449/) (2025)
- [Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics](https://mlsanity.com/paper/2510.12311/) (2025)
- [Statistical Finite Elements via Langevin Dynamics](https://mlsanity.com/paper/2110.11131/) (2021)
- [A sharp uniform-in-time error estimate for Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2207.09304/) (2022)
- [Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2305.15988/) (2023)
- [The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptions](https://mlsanity.com/paper/2502.03458/) (2025)
- [Uniform-in-time convergence bounds for Persistent Contrastive Divergence algorithms](https://mlsanity.com/paper/2510.01944/) (2025)
- [Generalization Bounds for Label Noise Stochastic Gradient Descent](https://mlsanity.com/paper/2311.00274/) (2023)
- [kTULA: A Langevin sampling algorithm with improved KL bounds under super-linear log-gradients](https://mlsanity.com/paper/2506.04878/) (2025)
- [Regime-Switching Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2509.00941/) (2025)
- [Anchored Langevin Algorithms](https://mlsanity.com/paper/2509.19455/) (2025)
- [Global convergence of optimized adaptive importance samplers](https://mlsanity.com/paper/2201.00409/) (2022)
- [Weak Convergence of Approximate reflection coupling and its Application to Non-convex Optimization](https://mlsanity.com/paper/2205.11970/) (2022)
- [Approximating Langevin Monte Carlo with ResNet-like Neural Network architectures](https://mlsanity.com/paper/2311.03242/) (2023)
- [Random Reshuffling for Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2501.16055/) (2025)
- [Geometric ergodicity of SGLD via reflection coupling](https://mlsanity.com/paper/2301.06769/) (2023)
- [Subsampling Error in Stochastic Gradient Langevin Diffusions](https://mlsanity.com/paper/2305.13882/) (2023)

## Abstract (arXiv)

In this paper, we are concerned with a non-asymptotic analysis of sampling algorithms used in nonconvex optimization. In particular, we obtain non-asymptotic estimates in Wasserstein-1 and Wasserstein-2 distances for a popular class of algorithms called Stochastic Gradient Langevin Dynamics (SGLD). In addition, the aforementioned Wasserstein-2 convergence result can be applied to establish a non-asymptotic error bound for the expected excess risk. Crucially, these results are obtained under a local Lipschitz condition and a local dissipativity condition where we remove the uniform dependence in the data stream. We illustrate the importance of this relaxation by presenting examples from variational inference and from index tracking optimization.