---
title: "Subpolynomial-Query Proximal Sampling Beyond Log-Concavity"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.03442v1"
permalink: "https://feed.astralor.com/items/itm_11a17aff464f85fdd4fbe104"
published: "2026-11-02T16:55:28.000Z"
score: 57
channel: "ai"
tags: ["OpenAI","Subpolynomial-Query Proximal Sampling","Beyond Log-Concavity","Lipschitz","Our","Gaussian"]
---

# Subpolynomial-Query Proximal Sampling Beyond Log-Concavity

## 速览

We study the gradient query complexity of sampling from a density $π(x)\propto\mathrm{e}^{-V(x)}$ on $\mathbb{R}^d$, where $V$ has a $β$-Lipschitz gradient but need not be convex. Our approach uses the proximal sampler,…

## 关键点

- We study the gradient query complexity of sampling from a density $π(x)\propto\mathrm{e}^{-V(x)}$ on $\mathbb{R}^d$, where $V$ has a $β$-Lipschitz gradient but need not be convex.
- Our approach uses the proximal sampler, which alternates Gaussian perturbation with sampling a position conditional on the noisy observation.
- We implement its observation chain using the high-order noisy conditional sampler of [OpenAI 2026], obtaining improved dimension dependence under functional inequalities.

## 全文

We study the gradient query complexity of sampling from a density $π(x)\propto\mathrm{e}^{-V(x)}$ on $\mathbb{R}^d$, where $V$ has a $β$-Lipschitz gradient but need not be convex. Our approach uses the proximal sampler, which alternates Gaussian perturbation with sampling a position conditional on the noisy observation. We implement its observation chain using the high-order noisy conditional sampler of [OpenAI 2026], obtaining improved dimension dependence under functional inequalities. If $π$ satisfies a log-Sobolev inequality (LSI) with constant $α$, then for every fixed $ν>0$, there is a finite constant $C_ν$ depending only on $ν$ such that the algorithm returns a sample within total-variation distance $\varepsilon$ using at most $C_νκ(d+κ+\varepsilon^{-1}+\|\nabla V(x_0)\|^2/β)^ν$ queries, where $κ=β/α$ and $x_0$ is an arbitrary reference point for initialization. The analysis controls center-dependent local errors along exact proximal histories and removes the final observation noise by conditional decoding. Under a Poincaré inequality (PI), we obtain a corresponding guarantee from a warm start with a known bound on its Rényi divergence. An oracle lower bound shows that a stationary point alone, which suffices under LSI, is insufficient under PI.

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