Hyperparameter optimization plays a pivotal role in enhancing the predictive performance and generalization capabilities of ML models. However, in many applications, we do not only care about predictive performance but also about objectives such as inference time, memory, or energy consumption. In such MOO scenarios, determining the importance of hyperparameters poses a significant challenge due to the complex interplay between the conflicting objectives. In this paper, we propose the first method for assessing the importance of hyperparameters in the context of multi-objective hyperparameter optimization. Our approach leverages surrogate-based hyperparameter importance (HPI) measures, i.e. fANOVA and ablation paths, to provide insights into the impact of hyperparameters on the optimization objectives. Specifically, we compute the a-priori scalarization of the objectives and determine the importance of the hyperparameters for different objective tradeoffs. Through extensive empirical evaluations on diverse benchmark datasets with three different objectives paired with accuracy, namely time, demographic parity, and energy consumption, we demonstrate the effectiveness and robustness of our proposed method. Our findings not only offer valuable guidance for hyperparameter tuning in MOO tasks but also contribute to advancing the understanding of HPI in complex optimization scenarios.

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