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PreprintCC BY 4.0arXiv

Locally adaptive step sizes for Hamiltonian Monte Carlo methods

  • Jimmy Huy Tran
  • Tore Selland Kleppe
  • Nawaf Bou-Rabee
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Abstract

Exact reversible locally adaptive step sizes are introduced by Bou-Rabee et al. (2026) in the context of the No-U-Turn Hamiltonian Monte Carlo (HMC) sampler for the purpose of high performance HMC sampling in challenging target distributions. This paper carefully explains and illustrates the locally adaptive step size procedure under more general assumptions. Alternative error measures are introduced with the aim of further enhancing MCMC performance by reducing the prevalence of reversibility failure rejections. In addition, the paper shows how to introduce the locally adaptive step sizes also within standard HMC and Metropolis-corrected kinetic Langevin/generalized HMC (GHMC). Finally, a numerical study of the relative merits of the proposed error measures in the context of different Hamiltonian flow-based MCMC methods is provided.

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Cite

BibTeXRIS
BibTeX
@misc{tran2026locally,
  title = {{Locally adaptive step sizes for Hamiltonian Monte Carlo methods}},
  author = {Jimmy Huy Tran and Tore Selland Kleppe and Nawaf Bou-Rabee},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16506},
  eprint = {2610.16506},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16506},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Locally adaptive step sizes for Hamiltonian Monte Carlo methods
AU  - Jimmy Huy Tran
AU  - Tore Selland Kleppe
AU  - Nawaf Bou-Rabee
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16506
UR  - https://arxiv.org/abs/2610.16506
AB  - Exact reversible locally adaptive step sizes are introduced by Bou-Rabee et al. (2026) in the context of the No-U-Turn Hamiltonian Monte Carlo (HMC) sampler for the purpose of high performance HMC sampling in challenging target distributions. This paper carefully explains and illustrates the locally adaptive step size procedure under more general assumptions. Alternative error measures are introduced with the aim of further enhancing MCMC performance by reducing the prevalence of reversibility failure rejections. In addition, the paper shows how to introduce the locally adaptive step sizes also within standard HMC and Metropolis-corrected kinetic Langevin/generalized HMC (GHMC). Finally, a numerical study of the relative merits of the proposed error measures in the context of different Hamiltonian flow-based MCMC methods is provided.
ER  -