# Non-asymptotic estimates for accelerated high order Langevin Monte Carlo algorithms

arXiv: https://arxiv.org/abs/2405.05679 · HTML: https://mlsanity.com/paper/2405.05679/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2024.

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

- [kTULA: A Langevin sampling algorithm with improved KL bounds under super-linear log-gradients](https://mlsanity.com/paper/2506.04878/) (2025)

## Abstract (arXiv)

In this paper, we propose two new algorithms, namely, aHOLA and aHOLLA, to sample from high-dimensional target distributions with possibly super-linearly growing potentials. We establish non-asymptotic convergence bounds for aHOLA in Wasserstein-1 and Wasserstein-2 distances with rates of convergence equal to 1+q/2 and 1/2+q/4, respectively, under a local H"older condition with exponent q∈(0,1] and a convexity at infinity condition on the potential of the target distribution. Similar results are obtained for aHOLLA under certain global continuity conditions and a dissipativity condition. Crucially, we achieve state-of-the-art rates of convergence of the proposed algorithms in the non-convex setting which are higher than those of the existing algorithms. Examples from high-dimensional sampling and logistic regression are presented, and numerical results support our main findings.