This paper presents a new approach for batch Bayesian Optimization (BO) called Thompson Sampling-Regret to Sigma Ratio directed sampling (TS-RSR), where we sample a new batch of actions by minimizing a Thompson Sampling approximation of a regret to uncertainty ratio. Our sampling objective is able to coordinate the actions chosen in each batch in a way that minimizes redundancy between points whilst focusing on points with high predictive means or high uncertainty. Theoretically, we provide rigorous convergence guarantees on our algorithm's regret, and numerically, we demonstrate that our method attains state-of-the-art performance on a range of challenging synthetic and realistic test functions, where it outperforms several competitive benchmark batch BO algorithms.

翻译：本文提出了一种新颖的批量贝叶斯优化方法，称为TS-RSR（Thompson Sampling-Regret to Sigma Ratio directed sampling），其通过最小化遗憾-不确定性比值的汤普森采样近似值来采样新的批量动作。我们的采样目标能够协调每批中选定的动作，在最小化各点冗余性的同时，聚焦于具有高预测均值或高不确定性的区域。在理论层面，我们为该算法的遗憾值提供了严格的收敛性保证；在数值实验层面，我们证明该方法在一系列具有挑战性的合成与真实测试函数上达到了最先进的性能，显著优于多个具有竞争力的基准批量贝叶斯优化算法。