# On the Dissipation of Ideal Hamiltonian Monte Carlo Sampler

arXiv: https://arxiv.org/abs/2209.07438 · HTML: https://mlsanity.com/paper/2209.07438/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 17 references that are in the map.
- First posted on arXiv 15 Sep 2022.

## Builds on (most cited first, 5 of 5)

- [On sampling from a log-concave density using kinetic Langevin diffusions](https://mlsanity.com/paper/1807.09382/) (2018)
- [Optimal Convergence Rate of Hamiltonian Monte Carlo for Strongly Logconcave Distributions](https://mlsanity.com/paper/1905.02313/) (2019)
- [Mixing Time Guarantees for Unadjusted Hamiltonian Monte Carlo](https://mlsanity.com/paper/2105.00887/) (2021)
- [An Introduction to Hamiltonian Monte Carlo Method for Sampling](https://mlsanity.com/paper/2108.12107/) (2021)
- [Accelerating Hamiltonian Monte Carlo via Chebyshev Integration Time](https://mlsanity.com/paper/2207.02189/) (2022)

## Built on by (most cited first, 1 of 1)

- [Hamiltonian Monte Carlo for efficient Gaussian sampling: long and random steps](https://mlsanity.com/paper/2209.12771/) (2022)

## Abstract (arXiv)

We report on what seems to be an intriguing connection between variable integration time and partial velocity refreshment of Ideal Hamiltonian Monte Carlo samplers, both of which can be used for reducing the dissipative behavior of the dynamics. More concretely, we show that on quadratic potentials, efficiency can be improved through these means by a √kappa factor in Wasserstein-2 distance, compared to classical constant integration time, fully refreshed HMC. We additionally explore the benefit of randomized integrators for simulating the Hamiltonian dynamics under higher order regularity conditions.