In this talk we present a computational complexity analysis for optimization problems where the objective function value can only be estimated with errors at any decision point. In particular, we study two different settings. In the first setting, the model is basically stochastic programming, but only one sample is taken at each decision point. In the second setting, the objective value can be estimated arbitrarily close to the true value, but at a cost that is increasing with regard to the inverse of the precision desired. Furthermore, we discuss extensions of the analysis to a general constrained model with a composite objective function, consisting of the vague objective and a non-smooth regularizer.