改进黑箱优化中顺序查询的协方差估计，提升收敛精度。
Ruppert-Polyak averaging for Stochastic Order Oracle
- 基于相对比较构建更精准的协方差矩阵估计方法。
- 理论分析显示收敛速率优于现有方法。
- 适合关注黑箱优化收敛性与稳定性研究者。
黑箱优化领域因缺乏目标函数内部机制信息而面临挑战。一种有前景的解决方案是随机顺序查询（Stochastic Order Oracle）概念。该方法仅依赖函数值的相对比较，无需精确值。本文提出了一种新型、更优的协方差矩阵估计方法，用于提升随机顺序查询的渐近收敛性分析。相较于现有研究，本方法在收敛速率估计上更具准确性。数值实验验证了理论结果，为所提方法提供了强有力的实证支持。
原文摘要 · Abstract (English)
Black-box optimization, a rapidly growing field, faces challenges due to limited knowledge of the objective function's internal mechanisms. One promising approach to address this is the Stochastic Order Oracle Concept. This concept, similar to other Order Oracle Concepts, relies solely on relative comparisons of function values without requiring access to the exact values. This paper presents a novel, improved estimation of the covariance matrix for the asymptotic convergence of the Stochastic Order Oracle Concept. Our work surpasses existing research in this domain by offering a more accurate estimation of asymptotic convergence rate. Finally, numerical experiments validate our theoretical findings, providing strong empirical support for our proposed approach.
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