# Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case

arXiv: https://arxiv.org/abs/2301.08039 · HTML: https://mlsanity.com/paper/2301.08039/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 30 references that are in the map.
- First posted on arXiv 19 Jan 2023.

## Builds on (most cited first, 18 of 18)

- [Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis](https://mlsanity.com/paper/1702.03849/) (2017)
- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [Underdamped Langevin MCMC: A non-asymptotic analysis](https://mlsanity.com/paper/1707.03663/) (2017)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [Sharp convergence rates for Langevin dynamics in the nonconvex setting](https://mlsanity.com/paper/1805.01648/) (2018)
- [On sampling from a log-concave density using kinetic Langevin diffusions](https://mlsanity.com/paper/1807.09382/) (2018)
- [The promises and pitfalls of Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/1811.10072/) (2018)
- [Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimization](https://mlsanity.com/paper/1910.02008/) (2019)
- [The Tamed Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1710.05559/) (2017)
- [Global Convergence of Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Stochastic Optimization: Non-Asymptotic Performance Bounds and Momentum-Based Acceleration](https://mlsanity.com/paper/1809.04618/) (2018)
- [Taming neural networks with TUSLA: Non-convex learning via adaptive stochastic gradient Langevin algorithms](https://mlsanity.com/paper/2006.14514/) (2020)
- [On stochastic gradient Langevin dynamics with dependent data streams in the logconcave case](https://mlsanity.com/paper/1812.02709/) (2018)
- [Nonasymptotic analysis of Stochastic Gradient Hamiltonian Monte Carlo under local conditions for nonconvex optimization](https://mlsanity.com/paper/2002.05465/) (2020)
- [Breaking Reversibility Accelerates Langevin Dynamics for Global Non-Convex Optimization](https://mlsanity.com/paper/1812.07725/) (2018)
- [Stochastic Gradient Hamiltonian Monte Carlo for Non-Convex Learning](https://mlsanity.com/paper/1903.10328/) (2019)
- [First-Order Algorithms Without Lipschitz Gradient: A Sequential Local Optimization Approach](https://mlsanity.com/paper/2010.03194/) (2020)
- [Proximal mappings and Moreau envelopes of single-variable convex piecewise cubic functions and multivariable gauge functions](https://mlsanity.com/paper/1909.05795/) (2019)

## Built on by (most cited first, 12 of 12)

- [Improved Discretization Analysis for Underdamped Langevin Monte Carlo](https://mlsanity.com/paper/2302.08049/) (2023)
- [Taming under isoperimetry](https://mlsanity.com/paper/2311.09003/) (2023)
- [Central Limit Theorem for Two-Timescale Stochastic Approximation with Markovian Noise: Theory and Applications](https://mlsanity.com/paper/2401.09339/) (2024)
- [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)
- [The Performance Of The Unadjusted Langevin Algorithm Without Smoothness Assumptions](https://mlsanity.com/paper/2502.03458/) (2025)
- [kTULA: A Langevin sampling algorithm with improved KL bounds under super-linear log-gradients](https://mlsanity.com/paper/2506.04878/) (2025)
- [Mean-field underdamped Langevin dynamics and its spacetime discretization](https://mlsanity.com/paper/2312.16360/) (2023)
- [Error estimates for tamed Euler and Randomized Euler schemes for SDEs with locally Lipschitz drift with applications to non-logconcave sampling and optimization](https://mlsanity.com/paper/2605.24937/) (2026)
- [Contractive kinetic Langevin samplers beyond global Lipschitz continuity](https://mlsanity.com/paper/2509.12031/) (2025)
- [Analysis of kinetic Langevin Monte Carlo under the stochastic exponential Euler discretization from underdamped all the way to overdamped](https://mlsanity.com/paper/2510.03949/) (2025)
- [Muon meets Tamed Langevin: Momentum Preconditioning beyond Convex and gradient-Lipschitz Potentials](https://mlsanity.com/paper/2610.02158/) (2026)

## Abstract (arXiv)

In this article we consider sampling from log concave distributions in Hamiltonian setting, without assuming that the objective gradient is globally Lipschitz. We propose two algorithms based on monotone polygonal (tamed) Euler schemes, to sample from a target measure, and provide non-asymptotic 2-Wasserstein distance bounds between the law of the process of each algorithm and the target measure. Finally, we apply these results to bound the excess risk optimization error of the associated optimization problem.