Dimension-independent convergence rate for non-isotropic (1,\lambda)-ES
Anne Auger, Claude LeBris and Marc Schoenauer
In: GECCO 2003, July 2003, Chicago.
Based on the theory of non-negative supermartingales,
convergence results are proven for adaptive $(1,\lambda)-ES$
(i.e. with Gaussian mutations), and geometrical convergence rates are
derived. In the $d$-dimensional case ($d > 1$), the algorithm studied
here uses a
different step-size update in each direction. However, the critical
value for the step-size, and the resulting convergence rate do not
depend on the dimension. Those results are discussed with respect to
previous work. Finally, rigourous numerical investigations on some
1-dimensional functions validate the theoretical results.