Bayesian Optimization Finds Robust Satisficing Solutions

Many design and optimization tasks can be framed as finding the best solution for a black-box function, often tackled with Bayesian optimization to minimize trials. However, in real-world scenarios, an absolute optimum isn't always necessary; a "satisficing" solution that meets certain criteria (e.g., "durable enough") is often sufficient. When multiple such satisfactory solutions exist, the question arises: which one to choose? This research proposes that robustness to input perturbations is a crucial criterion for selecting among satisficing solutions. These perturbations can occur once a solution is deployed, making a robust design more reliable in practice. The paper introduces a novel Bayesian optimization method specifically designed to efficiently locate satisficing solutions that are maximally robust to such variations. Unlike previous work, this method assumes precise control over inputs during the optimization phase but anticipates perturbations post-deployment. By focusing on finding solutions within the "superlevel set" (all satisfactory solutions) that can withstand the largest possible perturbations, the approach ensures greater practical utility and reliability for deployed designs.