Fig. 1. Golem's approach to estimating robustness. (a) Effect of uncertain inputs on objective function evaluations. The true objective function is shown as a gray line. The probability distribution p(x̃_k) of possible input value realizations for the targeted location x_k is shown in green, below the x-axis. The distribution of output f(x̃_k) values caused by the input uncertainty are similarly shown next to the y-axis. The expectation of f(x̃_k) is indicated by a green arrow. (b) Schematic of Golem's core concept. The yellow line represents the surrogate function used to model the underlying objective function, shown in the background as a gray line. This surrogate is built with a regression tree, trained on five observations (black crosses). Note how the observations f̃_k are noisy, due to the uncertainty in the location of the input queries. In the noiseless query setting, and assuming no measurement error, the observations would lie exactly on the underlying objective function. Vertical white, dashed lines indicate how this model has partitioned the one-dimensional input space. Given a target location x_k, the probability that the realized input was obtained from partition can be computed by integrating the probability density p(x̃_k) over , which is available analytically.