Section: New Results

Noisy Optimization Bounds with Constant Noise Variance

Many bounds in noisy evolutionary optimization are based on low variance assumptions (in particular, variance of noise converging to 0 close to the optima). Other bounds in the optimization literature consider difficult objective functions. We prove some new bounds, in the following setting[55] :

• without assuming that the variance is going to zero at the optimum;

• following some debates on the COCO mailing list (see 5.4 ), assuming that sampling far from the optimum (we had earlier results without this assumption; new results emphasize the contrast).