发表机构
Florida State University; Hong Kong University of Science and Technology (Guangzhou); Fudan University（佛罗里达州立大学; 香港科技大学（广州）; 复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对非光滑与重尾采样问题，提出非可逆锚定朗之万动力学（NALD）及非可逆反射锚定朗之万动力学（NRALD），通过打破可逆性实现更快收敛，数值实验验证了其效率。
AI 中文摘要
锚定朗之万动力学（Anchored Langevin dynamics, ALD）适用于目标分布密度可能不可微且为重尾分布的非光滑采样；反射锚定朗之万动力学（reflected anchored Langevin dynamics, RALD）可在约束域上对可能不可微的目标密度进行采样。本文中，我们提出并研究非可逆锚定朗之万动力学（non-reversible anchored Langevin dynamics, NALD），用于在欧氏空间中对可能不可微且为重尾的目标密度进行采样，以及非可逆反射锚定朗之万动力学（non-reversible reflected anchored Langevin dynamics, NRALD），用于在约束空间中对可能不可微的目标密度进行采样。我们的构造添加了由可能依赖状态的无散反对称矩阵场和流势产生的循环漂移，该构造无需目标密度的导数即可保持目标分布，允许随机时间变换表示，且适用于整个欧氏空间及具有法向反射的有界域。通过打破可逆性，我们通过有限时间非渐近收敛分析、大偏差分析和渐近方差缩减证明，NALD和NRALD可比其可逆对应算法更快收敛到目标分布。数值实验验证了所提算法的效率。
英文摘要
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.
Comments50 pages, 10 figures
