Bayesian Optimization is a popular approach for optimizing expensive
black-box functions. Its key idea is to use a surrogate model to approximate
the objective and, importantly, quantify the associated uncertainty that allows
a sequential search of query points that balance exploitation-exploration.
Gaussian process (GP) has been a primary candidate for the surrogate model,
thanks to its Bayesian-principled uncertainty quantification power and modeling
flexibility. However, its challenges have also spurred an array of alternatives
whose convergence properties could be more opaque. Motivated by these, we study
in this paper an axiomatic framework that elicits the minimal requirements to
guarantee black-box optimization convergence that could apply beyond GP-related
methods. Moreover, we leverage the design freedom in our framework, which we
call Pseudo-Bayesian Optimization, to construct empirically superior
algorithms. In particular, we show how using simple local regression, and a
suitable "randomized prior" construction to quantify uncertainty, not only
guarantees convergence but also consistently outperforms state-of-the-art
benchmarks in examples ranging from high-dimensional synthetic experiments to
realistic hyperparameter tuning and robotic applications.

采用拟贝叶斯优化的框架，通过利用简单的局部回归和随机化先验构建来量化不确定性，并保证收敛性，有效地优化高维度的综合实验、超参数调整和机器人应用的例子中胜过最先进的基准测试。