Model-based methods are popular in derivative-free optimization (DFO). In most of them, a single model function is built to approximate the objective function. This is generally based on the assumption that the objective function is one blackbox. However, some real-life and theoretical problems show that the objective function may consist of several blackboxes. In those problems, the information provided by each blackbox may not be equal. In this situation, one could build multiple sub-models that are then combined to become a final model. In this paper, we analyze the relation between the accuracy of those sub-models and the model constructed through their operations. We develop a broad framework that can be used as a theoretical tool in model error analysis and future research in DFO algorithms design.
翻译:基于模型的方法在无衍生物优化(DFO)中很受欢迎。在大多数情况下,一个单一的模型功能是用来估计目标功能的。这一般是基于一种假设,即目标功能是一个黑匣子。然而,一些现实生活和理论问题表明,目标功能可能由几个黑盒组成。在这些问题中,每个黑盒提供的信息可能不尽相同。在这种情况下,人们可以建立多个子模型,然后将其合并成最后模型。在本文中,我们分析了这些子模型的准确性与通过操作构建模型之间的关系。我们开发了一个广泛的框架,可以用作模型错误分析和DFO算法设计的未来研究的理论工具。