发表机构
Innopolis University; MIRAI; Kharkevich Institute for Information Transmission Problems RAS; HSE University（因诺波利斯大学; MIRAI; 俄罗斯科学院哈雷维奇信息传输问题研究所; 高等经济大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究带随机函数约束的凸随机优化问题，提出无梯度方法，在仅有噪声函数值可用时，分别统计顺序轮次、预言机调用和内部操作三种资源，适用于光滑或非光滑及强凸目标。
AI 中文摘要
我们研究了带有 $m$ 个期望约束的凸随机优化问题，即 $\u200b\u200b\\(\min\{f(x)=\E F(x,\xi):\\ g_i(x)=\E G_i(x,\xi)\le 0,\\ i=1,\dots,m,\\ x\in \Q\}\\)，当仅有噪声函数值可用时。每次调用时，预言机在两个点返回向量 $(F(x,\xi),G_1(x,\xi),\dots,G_m(x,\xi))$，且两点的 $\xi$ 实现相同（两点反馈）。数据可能是光滑或非光滑的，目标函数可能是强凸的。我们分别统计三种资源：\u200b\u200b\\(\emph{顺序预言机轮次} \Nseq\\)（可并行发送的查询批次）、\u200b\u200b\\(\emph{预言机调用}\\)，分为用于目标的调用和用于约束的调用，以及\u200b\u200b\\(\emph{内部操作}\\)，如近端步骤或与存储的雅可比样本的矩阵-向量乘积，这些操作不需要新的轮次。
英文摘要
We develop accelerated gradient-free methods for stochastic convex optimization with constraints defined by expectations. Our batched primal-dual sliding method uses two-point evaluations sharing a random sample and guarantees expected objective error and expected maximum constraint violation at most $\varepsilon$. It achieves $O(\varepsilon^{-1/2})$ sequential oracle rounds for smooth data and $O(d^{1/4}/\varepsilon)$ for nonsmooth data in dimension $d$, recovering the accuracy and dimension dependence of the corresponding unconstrained accelerated methods. The smooth rate is optimal in accuracy. Each round collects all samples needed for its inner primal-dual updates. Total evaluations retain quadratic dependence on inverse accuracy, with only polylogarithmic dependence on the number of constraints under vector feedback. Complementary lower bounds distinguish the dimension cost of gradient estimation from the unavoidable logarithmic cost of estimating noisy constraint levels. For smooth strongly convex objectives, restarts give logarithmic round complexity and objective evaluation cost linear in inverse accuracy, while constraint-level estimation necessarily remains quadratic. Known affine constraints require no constraint-oracle calls.
