提出一种基于后验采样的改进方法，理论证明其累积后悔呈亚线性增长。
Regret Analysis of Posterior Sampling-Based Expected Improvement for Bayesian Optimization
- 用后验样本路径最大值代替传统期望提升，实现随机化优化策略
- 在高斯过程假设下，累积后悔达到亚线性增长，优于无界增长
- 适合需要理论保障的黑箱函数优化场景，如超参调优
贝叶斯优化是优化昂贵评估黑箱函数的强大工具。尽管期望提升（EI）在广泛应用场景中表现优异，但其理论分析仍远不及其他已建立的算法。本文分析了一种基于后验采样的随机化EI变体，该方法从后验样本路径的最大值中计算期望提升。我们证明，在黑箱函数服从高斯过程的假设下，该后验采样随机化EI可实现亚线性贝叶斯累积后悔。最后，通过数值实验验证了所提方法的有效性。
原文摘要 · Abstract (English)
Bayesian optimization is a powerful tool for optimizing an expensive-to-evaluate black-box function. In particular, the effectiveness of expected improvement (EI) has been demonstrated in a wide range of applications. However, theoretical analyses of EI are limited compared with other theoretically established algorithms. This paper analyzes a randomized variant of EI, which evaluates the EI from the maximum of the posterior sample path. We show that this posterior sampling-based random EI achieves the sublinear Bayesian cumulative regret bounds under the assumption that the black-box function follows a Gaussian process. Finally, we demonstrate the effectiveness of the proposed method through numerical experiments.
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