Maximally Robust Satisficing Bayesian Optimization

Standard Bayesian Optimization (BO) typically aims to find the global optimum of a black-box function. However, many real-world design tasks—such as material science or chemical synthesis—do not require the absolute best solution, but rather one that is 'satisficing' (i.e., meets a minimum quality threshold). Furthermore, these designs are often deployed in environments where input parameters are subject to noise or manufacturing tolerances. The authors address the problem of finding a solution that is not only satisficing but also maximally robust to these post-deployment perturbations, assuming that the optimization process itself can be conducted under controlled, noise-free conditions.

The authors propose MRSBO, which treats the 'robustness radius'—the maximum perturbation a solution can withstand while remaining above the threshold—as the primary objective. The algorithm uses an information-theoretic acquisition function that maximizes information gain about the robust maximizer and the robustness radius. By leveraging Random Fourier Features (RFF) to generate differentiable posterior samples, the method efficiently approximates the superlevel set and uses gradient-based optimization to identify the most robust point. This approach avoids the wasteful evaluations common in adversarial methods that assume noise is present during the optimization phase itself.

Empirical results demonstrate that MRSBO significantly outperforms existing robust optimization baselines, such as AdveRS2, in both synthetic and real-world scenarios. By focusing evaluations on the boundaries of the superlevel set rather than wasting resources learning the function's behavior within the entire set, MRSBO achieves faster convergence and higher robustness. This work is particularly significant for engineering and scientific design, where fabrication tolerances or environmental variability often render theoretically optimal designs unreliable or unsafe in practice.