# Zeroth-order Logconcave Sampling

arXiv: https://arxiv.org/abs/2507.18021 · HTML: https://mlsanity.com/paper/2507.18021/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2025.

## Built on by (most cited first, 6 of 6)

- [A unified complexity bound for logconcave sampling](https://mlsanity.com/paper/2606.12694/) (2026)
- [Beyond the d2.5-mixing bound for Dikin walks on polytopes](https://mlsanity.com/paper/2607.13943/) (2026)
- [Spectral Gaps of Hit-and-Run and Coordinate Hit-and-Run](https://mlsanity.com/paper/2608.16878/) (2026)
- [On two proofs of d2 mixing of weighted Dikin walks](https://mlsanity.com/paper/2608.28566/) (2026)
- [Thin-shell stability of Gaussian cooling: logconcave sampling with sesteric complexity from a cold start](https://mlsanity.com/paper/2609.15884/) (2026)
- [Reflected Proximal Dynamics for Accelerated High-Accuracy Log-Concave Sampling](https://mlsanity.com/paper/2610.16248/) (2026)

## Abstract (arXiv)

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:ℝdrightarrowℝcup∞, 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 ∞-R'enyi divergence), and using annealing to generate such a warm start. Here, we address the natural and more general problem of using a q-R'enyi divergence warm start to generate a sample that is varepsilon-close in q-R'enyi divergence. Our first main result is an algorithm with this end-to-end guarantee with state-of-the-art complexity for q=widetildeOmega(1). Our second result shows how to generate a q-R'enyi divergence warm start directly via annealing, by maintaining q-R'enyi divergence throughout, thereby obtaining a streamlined analysis and improved complexity. Such results were previously known only under the stronger assumptions of smoothness and access to first-order oracles. We also show a lower bound for Gaussian annealing by disproving a geometric conjecture about quadratic tilts of isotropic logconcave distributions. Central to our approach, we establish hypercontractivity of the heat adjoint and translate this into improved mixing time guarantees for the Proximal Sampler. The resulting analysis of both sampling and annealing follows a simplified and natural path, directly tying convergence rates to isoperimetric constants of the target distribution.