TY - GEN
T1 - Log-linear convergence and optimal bounds for the (1 + 1)-ES
AU - Jebalia, Mohamed
AU - Auger, Anne
AU - Liardet, Pierre
PY - 2008/6/9
Y1 - 2008/6/9
N2 - The (1 + 1)-ES is modeled by a general stochastic process whose asymptotic behavior is investigated. Under general assumptions, it is shown that the convergence of the related algorithm is sub-log-linear, bounded below by an explicit log-linear rate. For the specific case of spherical functions and scale-invariant algorithm, it is proved using the Law of Large Numbers for orthogonal variables, that the linear convergence holds almost surely and that the best convergence rate is reached. Experimental simulations illustrate the theoretical results.
AB - The (1 + 1)-ES is modeled by a general stochastic process whose asymptotic behavior is investigated. Under general assumptions, it is shown that the convergence of the related algorithm is sub-log-linear, bounded below by an explicit log-linear rate. For the specific case of spherical functions and scale-invariant algorithm, it is proved using the Law of Large Numbers for orthogonal variables, that the linear convergence holds almost surely and that the best convergence rate is reached. Experimental simulations illustrate the theoretical results.
UR - https://www.scopus.com/pages/publications/44649138810
U2 - 10.1007/978-3-540-79305-2_18
DO - 10.1007/978-3-540-79305-2_18
M3 - Conference contribution
AN - SCOPUS:44649138810
SN - 3540793046
SN - 9783540793045
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 207
EP - 218
BT - Artificial Evolution - 8th International Conference Evolution Artificielle, EA 2007, Revised Selected Papers
T2 - 8th International Conference on Artificial Evolution, EA 2007
Y2 - 29 October 2007 through 31 October 2007
ER -