The performance of any Machine Learning (ML) algorithm is impacted by the choice of its hyperparameters. As training and evaluating a ML algorithm is usually expensive, the hyperparameter optimization (HPO) method needs to be computationally efficient to be useful in practice. Most of the existing approaches on multi-objective HPO use evolutionary strategies and metamodel-based optimization. However, few methods have been developed to account for uncertainty in the performance measurements. This paper presents results on multi-objective hyperparameter optimization with uncertainty on the evaluation of ML algorithms. We combine the sampling strategy of Tree-structured Parzen Estimators (TPE) with the metamodel obtained after training a Gaussian Process Regression (GPR) with heterogeneous noise. Experimental results on three analytical test functions and three ML problems show the improvement over multi-objective TPE and GPR, achieved with respect to the hypervolume indicator.

Hyperparameter optimization constitutes a large part of typical modern machine learning workflows. This arises from the fact that machine learning methods and corresponding preprocessing steps often only yield optimal performance when hyperparameters are properly tuned. But in many applications, we are not only interested in optimizing ML pipelines solely for predictive accuracy; additional metrics or constraints must be considered when determining an optimal configuration, resulting in a multi-objective optimization problem. This is often neglected in practice, due to a lack of knowledge and readily available software implementations for multi-objective hyperparameter optimization. In this work, we introduce the reader to the basics of multi-objective hyperparameter optimization and motivate its usefulness in applied ML. Furthermore, we provide an extensive survey of existing optimization strategies, both from the domain of evolutionary algorithms and Bayesian optimization. We illustrate the utility of MOO in several specific ML applications, considering objectives such as operating conditions, prediction time, sparseness, fairness, interpretability and robustness.