提出可保证高概率最优解的贝叶斯优化停止准则
Regret-Based $(ε,δ)$-optimal Stopping Criteria for Bayesian Optimization
- 基于紧致置信上界推导更优瞬时后悔界
- 在1-δ概率下确保解距最优值不超过ε
- 适合追求理论保证的黑箱优化场景
贝叶斯优化（BO）是一种广泛使用的迭代黑箱优化方法，通常依赖高斯过程（GP）代理模型。实践中，BO常在固定评估预算后终止，这可能导致不必要的成本，且无法保证解的质量。尽管近期研究在实用停止准则方面取得进展，但理论严谨的停止准则仍不成熟。本文为任意迭代时刻的GP-UCB方法推导出更紧的瞬时后悔界，并基于此提出新的停止准则，确保在终止时以高概率1-δ获得ε-最优解。通过数值实验验证了所提准则的有效性与效率。
原文摘要 · Abstract (English)
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.
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