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

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) $ Rényi 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.

Statistics Theory (math.ST); Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG); Probability (math.PR); Machine Learning (stat.ML)

arXiv:2609.06905 [math.ST]

(or arXiv:2609.06905v1 [math.ST] for this version)

https://doi.org/10.48550/arXiv.2609.06905 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.