Accelerated High-Accuracy Sampling from a Warm Start via the Proximal Bouncy Particle Sampler

2026-09-07

AI Summary

本文研究了从特定分布中高效采样的问题，提出了一种结合近端采样器和反弹粒子采样器思想的新方法——近端反弹粒子采样器（Proximal BPS），通过该方法可快速获得与目标分布接近的样本。

Abstract

We study the problem of sampling from $\mu(\mathrm{d}x)\propto e^{-V(x)}\,\mathrm{d}x$ on $\mathbb{R}^d$, where $V$ is $\alpha$-strongly convex and $\beta$-smooth, and write $\kappa:=\beta/\alpha$. We design and analyze the Proximal Bouncy Particle Sampler (Proximal BPS), a new sampler that combines ideas from the proximal sampler and the bouncy particle sampler. From a warm start initialization with $ O(1) $ R\'enyi divergence w.r.t. $\mu$, Proximal BPS returns a sample whose law is $\varepsilon$-close to $\mu$ in total variation distance using $\widetilde O(\sqrt\kappa\,d^{1/4} \,\mathrm{polylog}(1/\varepsilon))$ gradient queries in expectation.

Problem

• sampling
• strongly convex
• smooth
• Rényi divergence
• total variation distance

Innovation

• Proximal Bouncy Particle Sampler
• proximal sampler
• bouncy particle sampler
• warm start initialization