Optimum-statistical Collaboration Towards Efficient Black-boxOptimization

We propose a general optimum-statistical collaboration framework for sequential black-box optimization. Based on general definitions of the resolution descriptor and the uncertainty quantifier, we provide a general regret analysis of the proposed framework. We then show that the proposed framework can be applied to a broader range of functions that have different smoothness, and it inspires tighter measures of the statistical uncertainty and thus a faster algorithm.