# Optimizing The Integrator Step Size for Hamiltonian Monte Carlo

arXiv: https://arxiv.org/abs/1411.6669 · HTML: https://mlsanity.com/paper/1411.6669/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2014.

## Built on by (most cited first, 8 of 8)

- [A Survey of Monte Carlo Methods for Parameter Estimation](https://mlsanity.com/paper/2107.11820/) (2021)
- [When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?](https://mlsanity.com/paper/2304.04724/) (2023)
- [GIST: Gibbs self-tuning for locally adaptive Hamiltonian Monte Carlo](https://mlsanity.com/paper/2404.15253/) (2024)
- [An Introduction to Hamiltonian Monte Carlo Method for Sampling](https://mlsanity.com/paper/2108.12107/) (2021)
- [Randomized Physics-Informed Machine Learning for Uncertainty Quantification in High-Dimensional Inverse Problems](https://mlsanity.com/paper/2312.06177/) (2023)
- [Hamiltonian Monte Carlo on ReLU Neural Networks is Inefficient](https://mlsanity.com/paper/2410.22065/) (2024)
- [Understanding the Trade-offs in Accuracy and Uncertainty Quantification: Architecture and Inference Choices in Bayesian Neural Networks](https://mlsanity.com/paper/2503.11808/) (2025)
- [Posterior sampling by source-space MCMC via prior-based few-step transport maps](https://mlsanity.com/paper/2610.01034/) (2026)

## Abstract (arXiv)

Hamiltonian Monte Carlo can provide powerful inference in complex statistical problems, but ultimately its performance is sensitive to various tuning parameters. In this paper we use the underlying geometry of Hamiltonian Monte Carlo to construct a universal optimization criteria for tuning the step size of the symplectic integrator crucial to any implementation of the algorithm as well as diagnostics to monitor for any signs of invalidity. An immediate outcome of this result is that the suggested target average acceptance probability of 0.651 can be relaxed to 0.6 lesssim a lesssim 0.9 with larger values more robust in practice.