Convergence results for the (1,lambda)-SA-ES using the theory of phi-irreducible Markov chains
This paper investigates theoretically the (1, &lambda;)-SA-ES on the well known sphere function. We prove sufficient conditions on the parameters of the algorithm ensuring the convergence of 1/n ln(&PAR; Xn &PAR;), where X-n is the parent at generation n. This in turn guarantees the asymptotic log-linear convergence or divergence of the algorithm. The technique used for this analysis calls upon the theory of Markov chains on a continuous state space and on the so-called Foster-Lyapunov drift conditions. Those conditions enable us to derive practical conditions that prove stability properties of Markov chains. &COPY; 2005 Elsevier B.V. All rights reserved.
convergence markov chains foster-lyapunov drift conditions evolution strategies