Convergence and non-asymptotic error analysis for kinetic Langevin samplers using the exact harmonic Langevin integrator

2026/05/22 by Katharina Schuh · 1 voice
Mathematics · #math.NA #math.PR #stat.CO

paper · pdf · doi:10.48550/arxiv.2605.24070

Abstract

We propose a novel kinetic Langevin sampler based on a specific splitting scheme using the exact harmonic Langevin integrator. For strongly log-concave target measures, the sampler exploits a decomposition of the strongly convex potential into a quadratic part and a convex perturbation with Lipschitz continuous gradient. For the resulting first- and second-order schemes associated with this splitting we establish convergence rates in L²-Wasserstein distance as well as non-asymptotic error bounds. In particular, the contraction rate is of the same order as that of the underlying continuous dynamics. To achieve ε-accuracy, the required step size for the second-order scheme is comparable to that of established splitting schemes such as OBABO or UBU, which are widely used in machine learning and molecular dynamics.

Citations

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• The computation of averages from equilibrium and nonequilibrium Langevin molecular dynamics
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• Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare
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Discussions

• Katharina Schuh: Convergence and non-asymptotic error analysis for kinetic Langevin samplers using the exact harmonic Langevin integrator https://arxiv.org/abs/2605.24070 https://arxiv.org/pdf/2605.24 [bsky, 0 points, 0 comments]

Related

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• Bounding the error of discretized Langevin algorithms for non-strongly log-concave targets
• Contraction Rate Estimates of Stochastic Gradient Kinetic Langevin Integrators
• An Inertial Langevin Algorithm