Accelerating Non-Smooth and Heavy-Tailed Sampling
Abstract
Anchored Langevin dynamics (ALD) is useful for non-smooth sampling where the density of the target distribution is possibly non-differentiable and heavy-tailed; reflected anchored Langevin dynamics (RALD) can sample possibly non-differentiable target density on a constrained domain. In this paper, we propose and study non-reversible anchored Langevin dynamics (NALD) for sampling possibly non-differentiable and heavy-tailed target density in the Euclidean space and the non-reversible reflected anchored Langevin dynamics (NRALD) for sampling possibly non-differentiable target density in the constrained space. Our construction adds a circulation drift generated by a possibly state-dependent divergence-free skew-symmetric matrix field and a stream potential. It preserves the target distribution without requiring derivatives of target density, admits a random-time-change representation, and applies both on the whole Euclidean space and on bounded domains with normal reflection. By breaking reversibility, we show that NALD and NRALD can converge to their target distributions faster than their reversible counterparts via finite-time non-asymptotic convergence analysis, a large deviations analysis and asymptotic variance reduction. Numerical experiments demonstrate the efficiency of the proposed algorithms.
Related
- Rapid Mixing of Stereographic MCMC for Heavy-Tailed Sampling
- Limit theory for a class of non-stationary linear processes with weakly dependent heavy-tailed innovations
- Tight Heavy-Tailed Complexity Bounds for Optimizing Polyak--Łojasiewicz Objectives
- DynaSPLIT: Strong tail-optimal scheduling for the M/G/n with heavy-tailed job sizes
- Hypocoercivity of Tempered Bouncy Particle Samplers for Heavy-Tailed Targets
BibTeX
@misc{ali2026accelerating,
title = {{Accelerating Non-Smooth and Heavy-Tailed Sampling}},
author = {Pervez Ali and Xiaoyu Wang and Yingli Wang and Lingjiong Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11139},
eprint = {2610.11139},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11139},
}
RIS
TY - UNPB
TI - Accelerating Non-Smooth and Heavy-Tailed Sampling
AU - Pervez Ali
AU - Xiaoyu Wang
AU - Yingli Wang
AU - Lingjiong Zhu
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11139
UR - https://arxiv.org/abs/2610.11139
AB - Anchored Langevin dynamics (ALD) is useful for non-smooth sampling where the density of the target distribution is possibly non-differentiable and heavy-tailed; reflected anchored Langevin dynamics (RALD) can sample possibly non-differentiable target density on a constrained domain. In this paper, we propose and study non-reversible anchored Langevin dynamics (NALD) for sampling possibly non-differentiable and heavy-tailed target density in the Euclidean space and the non-reversible reflected anchored Langevin dynamics (NRALD) for sampling possibly non-differentiable target density in the constrained space. Our construction adds a circulation drift generated by a possibly state-dependent divergence-free skew-symmetric matrix field and a stream potential. It preserves the target distribution without requiring derivatives of target density, admits a random-time-change representation, and applies both on the whole Euclidean space and on bounded domains with normal reflection. By breaking reversibility, we show that NALD and NRALD can converge to their target distributions faster than their reversible counterparts via finite-time non-asymptotic convergence analysis, a large deviations analysis and asymptotic variance reduction. Numerical experiments demonstrate the efficiency of the proposed algorithms.
ER -