Regret-Based $(ε,δ)$-optimal Stopping Criteria for Bayesian Optimization
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| Format: | Preprint |
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2026
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| _version_ | 1866918516593000448 |
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| author | Wang, Haowei Wang, Jingyi Wei, Qiyu |
| author_facet | Wang, Haowei Wang, Jingyi Wei, Qiyu |
| contents | 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 $ε$-optimal solution with high probability $1-δ$ upon termination. Numerical experiments are performed to validate and demonstrate the effectiveness and efficiency of our stopping criteria. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_22561 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regret-Based $(ε,δ)$-optimal Stopping Criteria for Bayesian Optimization Wang, Haowei Wang, Jingyi Wei, Qiyu Machine Learning 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 $ε$-optimal solution with high probability $1-δ$ upon termination. Numerical experiments are performed to validate and demonstrate the effectiveness and efficiency of our stopping criteria. |
| title | Regret-Based $(ε,δ)$-optimal Stopping Criteria for Bayesian Optimization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.22561 |