"The results of this paper have influenced current methods of hyperparameter search in modern deep learning systems, [and the algorithm] continues to be a popular acquisition algorithm even after a decade. The theorems and lemmas of this paper are quoted in recent papers, and their proof technique is borrowed in follow-up papers. On the duo of technical depth and impact this paper clearly stands out."

"Bayesian optimization has become a powerful tool in many machine learning problems in the last 10 years.... the mathematical technique used in the proof influenced subsequent research significantly."

"This is a nice, original analysis that has influenced many subsequent papers on GP bandit optimization and Bayesian optimization, and underlies the convergence analysis in very many Bayesian Optimization papers. Hence, it has become a well-known paper, which has had influence both in theory and practice, due to the ongoing practical impact of Bayesian Optimization for experimental design, hyperparameter tuning and more."

"Bayesian optimization using Gaussian processes is an important technique for black-box hyperparameter tuning and autoML. However, there was no explicit finite sample convergence theory for this method. This paper treats Bayesian optimization as a bandit problem, and obtained a cumulative regret bound for GP-UCB in terms of the information gain. This leads to a first finite sample theoretical analysis for Bayesian optimization.... it will have significant long term impact both theoretically and practically."