The class of algorithms called Hessian Estimation Evolution Strategies (HE-ESs) update the covariance matrix of their sampling distribution by directly estimating the curvature of the objective function. The approach is practically efficient, as attested by respectable performance on the BBOB testbed, even on rather irregular functions. In this article, we formally prove two strong guarantees for the (1 + 4)-HE-ES, a minimal elitist member of the family: stability of the covariance matrix update, and as a consequence, linear convergence on all convex quadratic problems at a rate that is independent of the problem instance.

中文翻译：

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Hessian估计演化策略的收敛性分析

称为 Hessian Estimation Evolution Strategies (HE-ES) 的一类算法通过直接估计目标函数的曲率来更新其采样分布的协方差矩阵。该方法实际上是有效的，正如在 BBOB 测试台上的可观性能所证明的那样，即使在相当不规则的功能上也是如此。在本文中，我们正式证明了 (1 + 4)-HE-ES（该家族的最小精英成员）的两个强有力的保证：协方差矩阵更新的稳定性，以及因此在所有凸二次问题上的线性收敛与问题实例无关的速率。