Model selection is an integral problem of model based optimization techniques such as Bayesian optimization (BO). Current approaches often treat model selection as an estimation problem, to be periodically updated with observations coming from the optimization iterations. In this paper, we propose an alternative way to achieve both efficiently. Specifically, we propose a novel way of integrating model selection and BO for the single goal of reaching the function optima faster. The algorithm moves back and forth between BO in the model space and BO in the function space, where the goodness of the recommended model is captured by a score function and fed back, capturing how well the model helped convergence in the function space. The score function is derived in such a way that it neutralizes the effect of the moving nature of the BO in the function space, thus keeping the model selection problem stationary. This back and forth leads to quick convergence for both model selection and BO in the function space. In addition to improved sample efficiency, the framework outputs information about the black-box function. Convergence is proved, and experimental results show significant improvement compared to standard BO.

通过在模型空间和函数空间之间进行反馈，将模型选择与贝叶斯优化相结合，以更加高效地达到函数的极值，证明收敛性并在实验结果中显示与标准贝叶斯优化相比的显著改进。

超贝叶斯优化预测建模