Challenges of Interaction in Optimizing Mixed Categorical-Continuous Variables

• URL: http://arxiv.org/abs/2504.00491v1
• Date: Tue, 01 Apr 2025 07:31:54 GMT
• Title: Challenges of Interaction in Optimizing Mixed Categorical-Continuous Variables
• Authors: Youhei Akimoto, Xilin Gao, Ze Kai Ng, Daiki Morinaga,
• Abstract summary: CatCMA has been proposed as a method for optimizing mixed categorical-continuous variables.<n>We identify two types of variable interactions that make the problem particularly challenging for CatCMA.<n>We propose two algorithmic components: a warm-starting strategy and a hyper-representation technique.
• Score: 4.74607424425146
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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