# On stochastic gradient Langevin dynamics with dependent data streams in the logconcave case

arXiv: https://arxiv.org/abs/1812.02709 · HTML: https://mlsanity.com/paper/1812.02709/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2018.

## Built on by (most cited first, 20 of 20)

- [On diffusion-based generative models and their error bounds: The log-concave case with full convergence estimates](https://mlsanity.com/paper/2311.13584/) (2023)
- [Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case](https://mlsanity.com/paper/2301.08039/) (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)
- [Convergence Analysis of Schr"odinger-F"ollmer Sampler without Convexity](https://mlsanity.com/paper/2107.04766/) (2021)
- [Taming under isoperimetry](https://mlsanity.com/paper/2311.09003/) (2023)
- [Tamed Langevin sampling under weaker conditions](https://mlsanity.com/paper/2405.17693/) (2024)
- [Constrained Langevin Algorithms with L-mixing External Random Variables](https://mlsanity.com/paper/2205.14192/) (2022)
- [Langevin dynamics based algorithm e-THvarepsilonO POULA for stochastic optimization problems with discontinuous stochastic gradient](https://mlsanity.com/paper/2210.13193/) (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)
- [Unadjusted Langevin algorithm for sampling a mixture of weakly smooth potentials](https://mlsanity.com/paper/2112.09311/) (2021)
- [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)
- [Functional Central Limit Theorem and Strong Law of Large Numbers for Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2210.02092/) (2022)
- [On the strong stability of ergodic iterations](https://mlsanity.com/paper/2304.04657/) (2023)
- [Contractive kinetic Langevin samplers beyond global Lipschitz continuity](https://mlsanity.com/paper/2509.12031/) (2025)
- [Improved Analysis for Hessian-free High-resolution Monte Carlo Sampling](https://mlsanity.com/paper/2608.25052/) (2026)
- [Quantitative Convergence Analysis of Projected Stochastic Gradient Descent for Non-Convex Losses via the Goldstein Subdifferential](https://mlsanity.com/paper/2510.02735/) (2025)

## Abstract (arXiv)

We study the problem of sampling from a probability distribution π on rsetd which has a density wrt the Lebesgue measure known up to a normalization factor x mapsto rme-U(x) / intrsetd rme-U(y) rmd y. We analyze a sampling method based on the Euler discretization of the Langevin stochastic differential equations under the assumptions that the potential U is continuously differentiable, nabla U is Lipschitz, and U is strongly concave. We focus on the case where the gradient of the log-density cannot be directly computed but unbiased estimates of the gradient from possibly dependent observations are available. This setting can be seen as a combination of a stochastic approximation (here stochastic gradient) type algorithms with discretized Langevin dynamics. We obtain an upper bound of the Wasserstein-2 distance between the law of the iterates of this algorithm and the target distribution π with constants depending explicitly on the Lipschitz and strong convexity constants of the potential and the dimension of the space. Finally, under weaker assumptions on U and its gradient but in the presence of independent observations, we obtain analogous results in Wasserstein-2 distance.