  We propose a new uncertainty estimator for gradient-free optimisation of
black-box simulators using deep generative surrogate models. Optimisation of
these simulators is especially challenging for stochastic simulators and higher
dimensions. To address these issues, we utilise a deep generative surrogate
approach to model the black box response for the entire parameter space. We
then leverage this knowledge to estimate the proposed uncertainty based on the
Wasserstein distance - the Wasserstein uncertainty. This approach is employed
in a posterior agnostic gradient-free optimisation algorithm that minimises
regret over the entire parameter space. A series of tests were conducted to
demonstrate that our method is more robust to the shape of both the black box
function and the stochastic response of the black box than state-of-the-art
methods, such as efficient global optimisation with a deep Gaussian process
surrogate.
