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arXiv · 2310.07399

Randomized Runge-Kutta-Nystr\"om Methods for Unadjusted Hamiltonian and Kinetic Langevin Monte Carlo

Nawaf Bou-Rabee·Tore Selland Kleppe
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Abstract

We introduce $5/2$- and $7/2$-order $L^2$-accurate randomized Runge-Kutta-Nystr\"{o}m 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 $L^2$-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.

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Nawaf Bou-Rabee, Tore Selland Kleppe. 2023-10-11. Randomized Runge-Kutta-Nystr\"om Methods for Unadjusted Hamiltonian and Kinetic Langevin Monte Carlo. https://doi.org/10.1090/mcom%2F4061

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