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\"{o}lder condition with exponent $q\in(0,1]$ 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. Numerical experiments are conducted to sample from several distributions and the results support our main findings.

翻译：本文提出了两种新算法，即aHOLA和aHOLLA，用于从可能具有超线性增长势的高维目标分布中进行采样。我们在目标分布的势满足局部Hölder条件（指数q∈(0,1]）和无穷远处凸性条件下，建立了aHOLA在Wasserstein-1和Wasserstein-2距离下的非渐近收敛界，收敛速率分别为$1+q/2$和$1/2+q/4$。在一定的全局连续性和耗散条件下，我们获得了aHOLLA的类似结果。关键在于，在非凸设定下，所提算法达到了优于现有算法的先进收敛速率。我们通过从多个分布中进行采样的数值实验，验证了主要结论。