Bayesian Optimization (BO) is a powerful method for tackling expensive black-box optimization problems. As a sequential model-based optimization strategy, BO iteratively explores promising solutions until a predetermined budget, either iterations or time, is exhausted. The decision on when to terminate BO significantly influences both the quality of solutions and its computational efficiency. In this paper, we propose a simple, yet theoretically grounded, two-step method for automatically terminating BO. Our core concept is to proactively identify if the search is within a convex region by examining previously observed samples.

Bayesian Optimization (BO) is a powerful method for tackling expensive black-box optimization problems. As a sequential model-based optimization strategy, BO iteratively explores promising solutions until a predetermined budget, either iterations or time, is exhausted. The decision on when to terminate BO significantly influences both the quality of solutions and its computational efficiency. In this paper, we propose a simple, yet theoretically grounded, two-step method for automatically terminating BO. Our core concept is to proactively identify if the search is within a convex region by examining previously observed samples.