Contractive kinetic Langevin samplers beyond global Lipschitz continuity

2025/09/15 by Iosif Lytras, Panayotis Mertikopoulos, Lytras, Iosif +1
Biochemistry, Genetics and Molecular Biology · Chemistry · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Mass Spectrometry Techniques and Applications #Numerical Analysis (math.NA) #Probability (math.PR) #Spectroscopy Techniques in Biomedical and Chemical Research #Spectroscopy and Quantum Chemical Studies #math.NA #math.PR

paper · pdf · doi:10.48550/arxiv.2509.12031

openalex publication_date 2025/09/15 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

In this paper, we examine the problem of sampling from log-concave distributions with (possibly) superlinear gradient growth under kinetic (underdamped) Langevin algorithms. Using a carefully tailored taming scheme, we propose two novel discretizations of the kinetic Langevin SDE, and we show that they are both contractive and satisfy a log-Sobolev inequality. Building on this, we establish a series of non-asymptotic bounds in 2-Wasserstein distance between the law reached by each algorithm and the underlying target measure.

Citations

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Related

• Tamed Langevin sampling under weaker conditions
• On sampling from a log-concave density using kinetic Langevin diffusions
• Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case
• kTULA: A Langevin sampling algorithm with improved KL bounds under super-linear log-gradients
• Langevin Monte Carlo for strongly log-concave distributions: Randomized midpoint revisited