论文标题
通过Polyak-Ruppert平均，极值寻求控制的极快收敛率
Extremely Fast Convergence Rates for Extremum Seeking Control with Polyak-Ruppert Averaging
论文作者
论文摘要
随机近似是机器学习和优化中许多算法的基础。总体而言，收敛是慢速的：均方误差消失为$ o（n^{ - 1}）$。在许多应用中，称为准故事近似的确定性对应物是一种可行的替代方法，包括无梯度的优化和增强学习。在先前的研究中假定，最佳可实现的收敛速率为$ O（n^{ - 2}）$。本文显示，通过设计，可以通过$ o（n^{ - 4+δ}）$获得更快的收敛速度，并使用$δ> 0 $ intunary。首次引入两种技术来达到这种收敛速度。该理论也是在无梯度优化的背景下进行的，并根据标准基准进行了测试。主要结果是基于数字理论和根据随机近似理论适应的技术的新应用的结合。
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic approximation is a viable alternative in many applications, including gradient-free optimization and reinforcement learning. It was assumed in prior research that the optimal achievable convergence rate is $O(n^{-2})$. It is shown in this paper that through design it is possible to obtain far faster convergence, of order $O(n^{-4+δ})$, with $δ>0$ arbitrary. Two techniques are introduced for the first time to achieve this rate of convergence. The theory is also specialized within the context of gradient-free optimization, and tested on standard benchmarks. The main results are based on a combination of novel application of results from number theory and techniques adapted from stochastic approximation theory.
