Convergence and non-asymptotic error analysis for kinetic Langevin samplers using the exact harmonic Langevin integrator
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913157775097856 |
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| author | Schuh, Katharina |
| author_facet | Schuh, Katharina |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_24070 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convergence and non-asymptotic error analysis for kinetic Langevin samplers using the exact harmonic Langevin integrator Schuh, Katharina Computation Numerical Analysis Probability Primary 60J05, secondary 65C05, 65C40 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. |
| title | Convergence and non-asymptotic error analysis for kinetic Langevin samplers using the exact harmonic Langevin integrator |
| topic | Computation Numerical Analysis Probability Primary 60J05, secondary 65C05, 65C40 |
| url | https://arxiv.org/abs/2605.24070 |