Technology Category
Search and Optimization: Evolutionary ComputationMachine Learning: Evolutionary LearningReasoning under Uncertainty: Stochastic Optimization
A Superlinearly Convergent Evolution Strategy
🤖 AI Summary
Derivative-free optimization algorithms for smooth convex problems often suffer from slow convergence. Method: This paper proposes the Hessian-Estimation Evolution Strategy (HE-ES), the first evolutionary framework to systematically incorporate quasi-Newton principles: it replaces conventional non-elitist recombination with an estimated inverse square root of the Hessian, integrates a derivative-free trust-region mechanism, and adopts a gradient-free update strategy inspired by NEWUOA. Contribution/Results: HE-ES achieves superlinear convergence without requiring gradient information—a theoretical improvement over standard evolution strategies in convergence order. Empirical evaluation on canonical smooth convex benchmarks demonstrates significantly accelerated convergence and enhanced optimization efficiency. By unifying evolutionary search with quasi-Newton geometry, HE-ES effectively bridges the long-standing gap between derivative-free optimization and quasi-Newton theory.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Hybrid algorithm combining evolution strategy and quasi-Newton method
Estimates inverse square root of Hessian matrix iteratively
Achieves superlinear convergence for smooth convex problems
Innovation
Methods, ideas, or system contributions that make the work stand out.
Hybrid algorithm combining evolution strategy and quasi-Newton method
Estimates inverse square root of Hessian matrix iteratively
Replaces global recombination with quasi-Newton step
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