Convergence Analysis of the Hessian Estimation Evolution Strategy

IF 4.6 2区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Evolutionary Computation Pub Date : 2022-03-01 DOI:10.1162/evco_a_00295

Tobias Glasmachers;Oswin Krause

引用次数: 1

Abstract

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.

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Hessian估计进化策略的收敛性分析

一类称为Hessian估计进化策略（HE ES）的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，在BBOB测试台上的良好性能证明了这一点，即使在相当不规则的函数上也是如此。在本文中，我们正式证明了（1 + 4） HE-ES，家族中的一个最小精英成员：协方差矩阵更新的稳定性，因此，所有凸二次型问题的线性收敛速度与问题实例无关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Evolutionary Computation 工程技术-计算机：理论方法

CiteScore

6.40

自引率

1.50%

发文量

审稿时长

3 months

期刊介绍： Evolutionary Computation is a leading journal in its field. It provides an international forum for facilitating and enhancing the exchange of information among researchers involved in both the theoretical and practical aspects of computational systems drawing their inspiration from nature, with particular emphasis on evolutionary models of computation such as genetic algorithms, evolutionary strategies, classifier systems, evolutionary programming, and genetic programming. It welcomes articles from related fields such as swarm intelligence (e.g. Ant Colony Optimization and Particle Swarm Optimization), and other nature-inspired computation paradigms (e.g. Artificial Immune Systems). As well as publishing articles describing theoretical and/or experimental work, the journal also welcomes application-focused papers describing breakthrough results in an application domain or methodological papers where the specificities of the real-world problem led to significant algorithmic improvements that could possibly be generalized to other areas.