Zeroth-order Logconcave Sampling

ArXi:2507.18021v2 Announce Type: replace-cross We study the zeroth-order query complexity of sampling from a general logconcave distribution: given access to an evaluation oracle for a convex function $V:\mathbb{R}^{d}\rightarrow\mathbb{R}\cup\{\infty\}$, output a point from a distribution within $\varepsilon$-distance to the density proportional to $e^{-V}$. A long line of work provides efficient algorithms for this problem in TV distance, assuming a pointwise warm start (i.e., in $\infty$-R\'enyi divergence), and using annealing to generate such a warm start.