Optimization of mixed categorical-continuous variables is prevalent in real-world applications of black-box optimization. Recently, CatCMA has been proposed as a method for optimizing such variables and has demonstrated success in hyper-parameter optimization problems. However, it encounters challenges when optimizing categorical variables in the presence of interaction between continuous and categorical variables in the objective function. In this paper, we focus on optimizing mixed binary-continuous variables as a special case and identify two types of variable interactions that make the problem particularly challenging for CatCMA. To address these difficulties, we propose two algorithmic components: a warm-starting strategy and a hyper-representation technique. We analyze their theoretical impact on test problems exhibiting these interaction properties. Empirical results demonstrate that the proposed components effectively address the identified challenges, and CatCMA enhanced with these components, named ICatCMA, outperforms the original CatCMA.

翻译：混合类别-连续变量的优化在黑箱优化的实际应用中十分普遍。最近，CatCMA被提出作为优化此类变量的一种方法，并在超参数优化问题中取得了成功。然而，当目标函数中连续变量与类别变量之间存在交互作用时，CatCMA在优化类别变量方面遇到了挑战。本文聚焦于混合二元-连续变量优化这一特例，识别出两类使CatCMA面临特殊困难的变量交互作用。为应对这些难题，我们提出了两种算法组件：预热启动策略与超表征技术。我们分析了它们在具有这些交互特性的测试问题上产生的理论影响。实证结果表明，所提出的组件能有效应对已识别的挑战，而用这些组件增强后的CatCMA（命名为ICatCMA）性能优于原始CatCMA。