Analyzing the (1, λ) Evolution Strategy via Stochastic Approximation Methods | Zendy

George Yin | Zendy; Günter Rudolph | Zendy; Schwefel H.-P | Zendy

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Analyzing the (1, λ) Evolution Strategy via Stochastic Approximation Methods

Author(s) -

George Yin,

Günter Rudolph,

Schwefel H.-P

Publication year - 1995

Publication title -

evolutionary computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 82

eISSN - 1530-9304

pISSN - 1063-6560

DOI - 10.1162/evco.1995.3.4.473

Subject(s) - iterated function , stochastic approximation , convergence (economics) , mathematics , mathematical optimization , constant (computer programming) , stochastic process , approximation error , rate of convergence , computer science , algorithm , mathematical analysis , key (lock) , statistics , computer security , economics , programming language , economic growth

The main objective of this paper is to analyze the (1, λ) evolution strategy by use of stochastic approximation methods. Both constant and decreasing step size algorithms are studied. Convergence and estimation error bounds for the (1, λ) evolution strategy are developed. First the algorithm is converted to a recursively defined scheme of stochastic approximation type. Then the analysis is carried out by using the analytic tools from stochastic approximation. In lieu of examining the discrete iterates, suitably scaled sequences are defined. These interpolated sequences are then studied in detail. It is shown that the limits of the sequences have natural connections to certain continuous time dynamical systems.

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