A unified complexity bound for logconcave sampling
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Abstract (arXiv)
We give a simple, unified, and nearly tight bound for sampling arbitrary logconcave distributions from a warm start using the In-and-Out algorithm along with exponential lifting. The main new ingredient in the analysis is an improved bound on the Poincar'e constant of a lifted distribution. As a consequence, the resulting convergence rate is nearly tight for both constrained settings (e.g., Gaussian restricted to a convex body) and well-conditioned settings (e.g., strongly logconcave and smooth densities).
Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 8 of its 18 references that are in the map. First posted on arXiv 10 Jun 2026.
Builds on
8 of 18 references.
References · 8
- 2020Structured Logconcave Sampling with a Restricted Gaussian Oraclecited by 86
- 2022Improved analysis for a proximal algorithm for samplingcited by 73
- 2024In-and-Out: Algorithmic Diffusion for Sampling Convex Bodiescited by 19
- 2024Entropy contraction of the Gibbs sampler under log-concavitycited by 13
- 2024Sampling and Integration of Logconcave Functions by Algorithmic Diffusioncited by 12
- 2025Faster logconcave sampling from a cold start in high dimensioncited by 7
- 2021The entropic barrier is n-self-concordantcited by 6
- 2025Zeroth-order Logconcave Samplingcited by 6
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Citing papers per year: 2026: 3.
3 papers.