Regret-Based (epsilon,elta)-optimal Stopping Criteria for Bayesian Optimization

arXiv:2605.22561v1 Announce Type: new Abstract: 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. In this work, we present provably tighter instantaneous regret bounds for GP upper confidence bound (GP-UCB) at any given iteration. Then, we propose stopping criteria for GP-UCB based on this tighter bound that ensures an epsilon-optimal solution with high probability 1-elta upon termination. Numerical experiments are performed to validate and demonstrate the effectiveness and efficiency of our stopping criteria.

Source: arXiv cs.LG | 2026-05-23