Minimizing the Thompson Sampling Regret-to-Sigma Ratio (TS-RSR): a provably efficient algorithm for batch Bayesian Optimization

This paper presents a new approach for batch Bayesian Optimization (BO), where the sampling takes place by minimizing a Thompson Sampling approximation of a regret to uncertainty ratio. Our 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 nonconvex test functions, where it outperforms several competitive benchmark batch BO algorithms by an order of magnitude on average.