The Geometry of Efficient Nonconvex Sampling
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Abstract (arXiv)
We present an efficient algorithm for uniformly sampling from an arbitrary compact body X subset ℝn from a warm start under isoperimetry and a natural volume growth condition. Our result provides a substantial common generalization of known results for convex bodies and star-shaped bodies. The complexity of the algorithm is polynomial in the dimension, the Poincar'e constant of the uniform distribution on X and the volume growth constant of the set X.
Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 14 of its 37 references that are in the map. First posted on arXiv 26 Mar 2026.
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References · 14
- 2016Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Conditioncited by 526
- 2019Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Sufficescited by 224
- 2020Structured Logconcave Sampling with a Restricted Gaussian Oraclecited by 85
- 2022Improved analysis for a proximal algorithm for samplingcited by 72
- 2023Improved dimension dependence of a proximal algorithm for samplingcited by 29
- 2017Efficient Convex Optimization with Membership Oraclescited by 23
- 2021A Proximal Algorithm for Sampling from Non-smooth Potentialscited by 23
- 2022A Proximal Algorithm for Samplingcited by 21
- 2024In-and-Out: Algorithmic Diffusion for Sampling Convex Bodiescited by 18
- 2024Sampling and Integration of Logconcave Functions by Algorithmic Diffusioncited by 12
- 2020Reducing Isotropy and Volume to KLS: Faster Rounding and Volume Algorithmscited by 9
- 2025Faster logconcave sampling from a cold start in high dimensioncited by 7
2 more
- 2016Hit-and-Run for Sampling and Planning in Non-Convex Spacescited by 3
- 2025Oracle-based Uniform Sampling from Convex Bodiescited by 3
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