Randomized Runge-Kutta-Nystr"om Methods for Unadjusted Hamiltonian and Kinetic Langevin Monte Carlo
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Abstract (arXiv)
We introduce 5/2- and 7/2-order L2-accurate randomized Runge-Kutta-Nystr"om methods, tailored for approximating Hamiltonian flows within non-reversible Markov chain Monte Carlo samplers, such as unadjusted Hamiltonian Monte Carlo and unadjusted kinetic Langevin Monte Carlo. We establish quantitative 5/2-order L2-accuracy upper bounds under gradient and Hessian Lipschitz assumptions on the potential energy function. The numerical experiments demonstrate the superior efficiency of the proposed unadjusted samplers on a variety of well-behaved, high-dimensional target distributions.
Key facts. Cited by 1 paper in the map (data through 13 Oct 2026). Builds on 11 of its 46 references that are in the map. First posted on arXiv 11 Oct 2023.
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11 of 46 references.
References · 11
- 2017Underdamped Langevin MCMC: A non-asymptotic analysiscited by 132
- 2019The Randomized Midpoint Method for Log-Concave Samplingcited by 77
- 2018Sharp convergence rates for Langevin dynamics in the nonconvex settingcited by 67
- 2018On sampling from a log-concave density using kinetic Langevin diffusionscited by 61
- 2018Coupling and Convergence for Hamiltonian Monte Carlocited by 36
- 2017Geometric integrators and the Hamiltonian Monte Carlo methodcited by 25
- 2020On the Ergodicity, Bias and Asymptotic Normality of Randomized Midpoint Sampling Methodcited by 23
- 2021Mixing Time Guarantees for Unadjusted Hamiltonian Monte Carlocited by 18
- 2021Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimensioncited by 11
- 2020Connecting the Dots: Numerical Randomized Hamiltonian Monte Carlo with State-Dependent Event Ratescited by 8
- 2022Unadjusted Hamiltonian MCMC with Stratified Monte Carlo Time Integrationcited by 8
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1 paper.