论文标题
元变量和分类变量的约束混合变量黑框优化问题的一般数学框架
A general mathematical framework for constrained mixed-variable blackbox optimization problems with meta and categorical variables
论文作者
论文摘要
黑框优化上下文中介绍了用于建模的数学框架，用于建模受约束的混合变量优化问题。该框架引入了新的符号，并允许解决方案策略。符号框架允许对元变量进行明确有效的建模，从而有助于解决此类问题的解决方案。新的术语元变量用于描述影响哪些变量作用或非作用的变量：元变量可能会影响变量和约束的数量。解决方案策略的灵活性支持主要的黑框混合变量优化方法：直接搜索方法和基于替代的方法（贝叶斯优化）。符号系统和解决方案策略通过来自机器学习社区的超参数优化问题的示例来说明。
A mathematical framework for modelling constrained mixed-variable optimization problems is presented in a blackbox optimization context. The framework introduces a new notation and allows solution strategies. The notation framework allows meta and categorical variables to be explicitly and efficiently modelled, which facilitates the solution of such problems. The new term meta variables is used to describe variables that influence which variables are acting or nonacting: meta variables may affect the number of variables and constraints. The flexibility of the solution strategies supports the main blackbox mixed-variable optimization approaches: direct search methods and surrogate-based methods (Bayesian optimization). The notation system and solution strategies are illustrated through an example of a hyperparameter optimization problem from the machine learning community.
