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. We provide high-probability theoretical guarantees on the regret of our algorithm. Finally, 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：本文提出了一种名为TS-RSR（Thompson Sampling-Regret to Sigma Ratio directed sampling）的批量贝叶斯优化新方法。该方法通过最小化遗憾与不确定性比值的汤普森采样近似值来采样新一批动作。我们的采样目标能够协调每批中选择的动作，在减少各采样点之间冗余性的同时，聚焦于具有高预测均值或高不确定性的区域。我们为该算法的遗憾值提供了高概率理论保证。最后，数值实验表明，在多种具有挑战性的合成函数和真实测试函数上，该方法均达到了当前最优性能，并优于多个具有竞争力的基准批量贝叶斯优化算法。