论文标题
（1+1） - 进化策略的收敛速率与Lipschitz连续梯度及其单调转换具有强烈凸的功能
Convergence rate of the (1+1)-evolution strategy on locally strongly convex functions with lipschitz continuous gradient and their monotonic transformations
论文作者
论文摘要
进化策略（ES）是黑框连续优化的有希望的算法类别之一。尽管在应用方面取得了广泛的成功，但对其收敛速度的理论分析受到凸二次函数及其单调转换的限制。在这项研究中，（1+1）-ES在本地$ l $ -ly-strongly convex上具有$ u $ -lipsChitz连续梯度的函数的上限和下限是$ \ \ exp \ exp \ left（-chome） $ \ exp \ left（ - \ frac1d \ right）$。值得注意的是，对目标函数的数学属性（例如Lipschitz常数）的任何先验知识均未给出算法，而现有的无衍生化优化算法的现有分析则需要它们。
Evolution strategy (ES) is one of promising classes of algorithms for black-box continuous optimization. Despite its broad successes in applications, theoretical analysis on the speed of its convergence is limited on convex quadratic functions and their monotonic transformation. In this study, an upper bound and a lower bound of the rate of linear convergence of the (1+1)-ES on locally $L$-strongly convex functions with $U$-Lipschitz continuous gradient are derived as $\exp\left(-Ω_{d\to\infty}\left(\frac{L}{d\cdot U}\right)\right)$ and $\exp\left(-\frac1d\right)$, respectively. Notably, any prior knowledge on the mathematical properties of the objective function such as Lipschitz constant is not given to the algorithm, whereas the existing analyses of derivative-free optimization algorithms require them.
