Multi-objective Parameter Tuning with Dynamic Compositional Surrogate Models

Multi-objective parameter tuning is a highly-practical black-box optimization problem, in which the target system is expensive to evaluate. To identify well-performing solutions within the limited budget, a substitution of the target system with a surrogate model, its cheap-to-evaluate approximation, introduces immense benefits. Some surrogates may be more successful for particular objective functions, other at certain stages of optimization. Alas, most state-of-the-art approaches do not address this issue, requiring either to be selected at design time; or lack granularity, changing all models for all objective functions simultaneously. In this paper we provide an approach allowing to individually assign surrogate models to different objective functions and to dynamically combine them into multi-objective compositional surrogate models. To ensure a high prediction quality, our approach contains a model validation strategy based on the cross-validation principle. Moreover, we unite multiple compositional surrogates within a portfolio to even further increase the quality of the search process. Finally, we use the proposed validation strategy to enable a dynamic sampling plan, allowing to get high-quality solutions with even fewer evaluations. The evaluation with a WFG benchmark suite for multi-objective optimization showed that our approach outperforms existing multi-objective model-based approaches.