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 $L^2$-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 $\varepsilon$-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.
| Comments: | 36 pages, 4 figures |
| Subjects: | Computation (stat.CO); Numerical Analysis (math.NA); Probability (math.PR) |
| MSC classes: | Primary 60J05, secondary 65C05, 65C40 |
| Cite as: | arXiv:2605.24070 [stat.CO] |
| (or arXiv:2605.24070v1 [stat.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24070 arXiv-issued DOI via DataCite (pending registration) |
From: Katharina Schuh [view email]
[v1]
Fri, 22 May 2026 11:31:04 UTC (148 KB)
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