Application of Selection Rules to Statistical GlobalOptimization

We consider global optimization methods that are based on statistical modeling of the objective function: at each step of the optimization algorithm distribution of possible function values is deened for all candidate points and the next sampling point is selected in order to optimize average performance of the algorithm. It is diicult to estimate total eeect of sampling at a given point on algorithm performance. Therefore, the standard approach is to sample the point that maximizes a certain one-step utility function u(x). Because u(x) does not take into account eeects of future sampling, utility function is modiied based on heuristic considerations in order to make search more global. We suggest to consider optimization criterion that includes the cost of computations in the objective function. This setting allows us to compute utility function that maximizes total expected reward of sampling directly. Assuming non-adaptive model of the objective function, optimal utility function is based on the stopping values z (x). z policy can be applied to improve a number of statistical global optimization methods and to compare eeciency of diierent methods dynamically based on their stopping values.