Global Optimisation of Black-Box Functions with Generative Models in the Wasserstein Space
This work addresses optimization challenges for black-box simulators, which is incremental as it builds on existing surrogate model approaches.
The paper tackles the problem of gradient-free optimization for black-box simulators, especially in stochastic and high-dimensional settings, by proposing a new uncertainty estimator based on Wasserstein distance with deep generative surrogate models, resulting in improved robustness compared to state-of-the-art methods like efficient global optimization with deep Gaussian processes.
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.