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 paper 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.

翻译：被称为赫西安估计演变战略(HE-ESs)的算法类别通过直接估计客观功能的曲线来更新其抽样分布的共变矩阵。 这种方法在实际中是有效的,通过BBBB测试台的可贵性表现证明,即使功能不太正常,我们也证明了这一点。 在本文中,我们正式证明家庭最精英成员HE-ES的两个强有力的保证:共变矩阵更新的稳定性,以及因此,在所有共振四方问题上以独立于问题实例的速率线性趋同。