Regret-Based $(ε,δ)$-optimal Stopping Criteria for Bayesian Optimization

Fuente: arXiv
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Main Authors: Wang, Haowei, Wang, Jingyi, Wei, Qiyu
Format: Preprint
Published: 2026
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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
id 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