| Issue |
ESAIM: M2AN
Volume 57, Number 6, November-December 2023
|
|
|---|---|---|
| Page(s) | 3335 - 3371 | |
| DOI | https://doi.org/10.1051/m2an/2023083 | |
| Published online | 29 November 2023 | |
Optimal friction matrix for underdamped Langevin sampling
1
Department of Mathematics, Imperial College London, London, UK
2
CERMICS, École des Ponts Champs-sur-Marne, France
3
MATHERIALS, Inria Paris, Paris, France
* Corresponding author: martin.chak@sorbonne-universite.fr
Received:
25
August
2022
Accepted:
3
October
2023
We propose a procedure for optimising the friction matrix of underdamped Langevin dynamics when used for continuous time Markov Chain Monte Carlo. Starting from a central limit theorem for the ergodic average, we present a new expression of the gradient of the asymptotic variance with respect to friction matrix. In addition, we present an approximation method that uses simulations of the associated first variation/tangent process. Our algorithm is applied to a variety of numerical examples such as toy problems with tractable asymptotic variance, diffusion bridge sampling and Bayesian inference problems for high dimensional logistic regression.
Mathematics Subject Classification: 60J25 / 60J60
Key words: Asymptotic variance / self-tuning algorithm / Langevin dynamics / variance reduction / Poisson equation
© The authors. Published by EDP Sciences, SMAI 2023
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