A unified complexity bound for logconcave sampling
Yunbum Kook, Santosh S. Vempala
cs.DS cs.LG math.PR stat.ML
Abstract
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 Poincaré 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).
Topics
Classified with taxonomy v2 on Sat, 5 Sept 2026.