On the performance of evolution strategies on noisy PDQFs: Progress rate analysis

This paper analyzes the behavior of the (mu/mu_I,lambda) ES on a class of noisy positive definite quadratic forms (PDQFs). First the equations for the normalized progress rates are derived and then analyzed for constant normalized noise strength and constant (non-normalized) noise strength. Since in the latter case the strategy is not able to reach the optimum, formulas for the final distances to the optimizer (steady state) are derived. The theoretical predictions are then compared with empirical results. In both noise cases the influence of the strategy parameters will be investigated. Further, the equipartition conjecture is used to provide an alternative derivation of the steady state distances in the case of vanishing mutation strength.