Global Optimisation of Black-Box Functions with Generative Models in the Wasserstein Space

TL;DR

This paper introduces a Wasserstein distance-based uncertainty estimator for gradient-free optimization of black-box simulators, improving robustness in stochastic and high-dimensional settings using deep generative models.

Contribution

It presents a novel uncertainty estimation method leveraging Wasserstein distance within a deep generative surrogate framework for black-box optimization.

Findings

More robust to function shape variations

Outperforms state-of-the-art methods in stochastic settings

Effective in high-dimensional parameter spaces

Abstract

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.