One-Dimensional global optimization for observations with noise

A problem of one-dimensional global optimization in the presence of noise is considered. The approach is based on modeling the objective function as a standard Wiener process which is observed with independent Gaussian noise. An asymptotic bound for the average error is estimated for the nonadaptive strategy defined by a uniform grid. Experimental results consistent with the asymptotic results are presented. An adaptive algorithm is proposed and experimentally compared with the nonadaptive strategy with respect to the average error.