Fig. 2. One-dimensional example illustrating the probabilistic approach to robustness and Golem's behavior. The top panel shows how g(x), which is defined as changes as the standard deviation of normally-distributed input noise p(x̃) is increased. Note that the curve for σ(x) = 0 corresponds to the original objective function. The panels at the bottom show the robust merits of a finite set of samples as estimated by Golem from the objective function values.