Quality Gain Analysis of the Weighted Recombination Evolution Strategy on General Convex Quadratic Functions

International audienceWe investigate evolution strategies with weighted recombi-nation on general convex quadratic functions. We derive the asymptotic quality gain in the limit of the dimension to infinity, and derive the optimal recombination weights and the optimal step-size. This work is an extension of previous works where the asymptotic quality gain of evolution strategies with weighted recombination was derived on the infinite dimensional sphere function. Moreover, for a finite dimensional search space, we derive rigorous bounds for the quality gain on a general quadratic function. They reveal the dependency of the quality gain both in the eigenvalue distribution of the Hessian matrix and on the recombina-tion weights. Taking the search space dimension to infinity , it turns out that the optimal recombination weights are independent of the Hessian matrix, i.e., the recombination weights optimal for the sphere function are optimal for convex quadratic functions