提出一种高效且可证明最优的贝叶斯优化方法
Optimal-Point Variance Reduction For Bayesian Optimization With Regret Guarantee
- 基于后验采样与蒙特卡洛近似，实现快速计算
- 理论证明其期望简单遗憾随迭代趋于零
- 适合需要严格性能保证的优化任务
本文研究了一种单步前瞻贝叶斯优化（BO）方法及其理论保证。尽管熵搜索等单步前瞻方法在实践中表现良好，但通常依赖于计算上不可行的近似，且其遗憾界尚未充分建立。为此，本文提出一种名为最优点方差减少（OVR）的单步前瞻方法，仅需后验采样和蒙特卡洛近似即可实现。我们为OVR中的蒙特卡洛估计在输入域上建立了统一误差界。此外，通过引入轻微探索激励的正则化OVR，实现了趋于零的贝叶斯期望简单遗憾上界。最后，数值实验验证了OVR的有效性。
原文摘要 · Abstract (English)
This paper studies a one-step lookahead Bayesian optimization (BO) method and its theoretical guarantee. Although the empirical effectiveness of one-step lookahead BO methods, such as entropy search, has been studied extensively, they often rely on computationally intractable approximations, and their regret guarantees remain underdeveloped. Thus, this paper proposes a one-step lookahead BO method called optimal-point variance reduction (OVR), which requires only posterior sampling and Monte Carlo approximations. We obtain a uniform error bound over an input domain for the Monte Carlo estimation in OVR. Furthermore, we show that the regularized OVR, with the slight modification to promote exploration, achieves a vanishing Bayesian expected simple regret upper bound. Finally, we demonstrate the effectiveness of OVR through numerical experiments.
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