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arXiv · 2609.06905

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

Fan Chen·Sinho Chewi·Jianfeng Lu·Matthew S Zhang
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Abstract

We study the problem of sampling from $μ(\mathrm{d}x)\propto e^{-V(x)}\,\mathrm{d}x$ on $\mathbb{R}^d$, where $V$ is $α$-strongly convex and $β$-smooth, and write $κ:=β/α$. 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) $ Rényi divergence w.r.t. $μ$, Proximal BPS returns a sample whose law is $\varepsilon$-close to $μ$ in total variation distance using $\widetilde O(\sqrtκ\,d^{1/4} \,\mathrm{polylog}(1/\varepsilon))$ gradient queries in expectation.

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Fan Chen, Sinho Chewi, Jianfeng Lu, Matthew S Zhang. 2026-09-07. Accelerated High-Accuracy Sampling from a Warm Start via the Proximal Bouncy Particle Sampler. https://arxiv.org/abs/2609.06905

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