A Superlinearly Convergent Evolution Strategy

TL;DR

This paper introduces a hybrid optimization algorithm combining evolution strategies and quasi-Newton methods, achieving superlinear convergence and improved performance on smooth convex problems.

Contribution

It presents a novel hybrid algorithm that estimates the inverse square root of the Hessian, replacing traditional recombination with a quasi-Newton step for faster convergence.

Findings

Achieves superlinear convergence in numerical experiments

Outperforms traditional evolution strategies on smooth convex problems

Demonstrates effectiveness of Hessian estimation in derivative-free optimization

Abstract

We present a hybrid algorithm between an evolution strategy and a quasi Newton method. The design is based on the Hessian Estimation Evolution Strategy, which iteratively estimates the inverse square root of the Hessian matrix of the problem. This is akin to a quasi-Newton method and corresponding derivative-free trust-region algorithms like NEWUOA. The proposed method therefore replaces the global recombination step commonly found in non-elitist evolution strategies with a quasi-Newton step. Numerical results show superlinear convergence, resulting in improved performance in particular on smooth convex problems.