Regret-Based $(\epsilon,\delta)$-optimal Stopping Criteria for Bayesian Optimization

ArXi:2605.22561v1 Announce Type: new Bayesian optimization (BO) is a widely used iterative black-box optimization method that utilizes Gaussian process (GP) surrogate models. In practice, BO is typically terminated after a fixed evaluation budget is exhausted, which can incur unnecessary cost and provides no optimality guarantee on solution quality. Recent research in developing a practical stopping criterion has made empirical progress, yet a theoretically sound stopping criterion remains a work in progress.