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 $\exp\left(-\Omega_{d\to\infty}\left(\frac{L}{d\cdot U}\right)\right)$ 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.

翻译：进化策略（ES）是解决黑箱连续优化问题的一类重要算法。尽管其在实际应用中取得了广泛成功，但目前关于其收敛速度的理论分析主要局限于凸二次函数及其单调变换。本研究推导了(1+1)-ES在局部$L$-强凸函数（具有$U$-利普希茨连续梯度）上的线性收敛率的上界和下界，分别为$\exp\left(-\Omega_{d\to\infty}\left(\frac{L}{d\cdot U}\right)\right)$和$\exp\left(-\frac1d\right)$。值得注意的是，该算法无需目标函数数学性质（如利普希茨常数）的先验知识，而现有无导数优化算法的理论分析通常需要此类信息。