Learning Configurations for Data-Driven Multi-Objective Optimization

Zhiyang Chen, Hailong Yao, Xia Yin
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:9642-9663, 2025.

Abstract

Multi-objective optimization problems arise widely in various fields. In practice, multi-objective optimization is generally solved by heuristics with tunable parameters that are highly application-specific. Tuning parameters based on real-world instances (a.k.a. algorithm configuration) are generally empirical without theoretical guarantees. In this work, we establish the theoretical foundation of data-driven multi-objective optimization through the lens of machine learning theory. We provide generalization guarantees on selecting parameters for multi-objective optimization algorithms based on sampled problem instances. Moreover, if the performance metric of the algorithm is the Pareto volume, we can PAC-learn the approximately optimal configuration in polynomial time. We apply our framework to various algorithms, including approximation algorithms, local search, and linear programming. Experiments on multiple problems verify our theoretical findings.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-chen25ce, title = {Learning Configurations for Data-Driven Multi-Objective Optimization}, author = {Chen, Zhiyang and Yao, Hailong and Yin, Xia}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {9642--9663}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/chen25ce/chen25ce.pdf}, url = {https://proceedings.mlr.press/v267/chen25ce.html}, abstract = {Multi-objective optimization problems arise widely in various fields. In practice, multi-objective optimization is generally solved by heuristics with tunable parameters that are highly application-specific. Tuning parameters based on real-world instances (a.k.a. algorithm configuration) are generally empirical without theoretical guarantees. In this work, we establish the theoretical foundation of data-driven multi-objective optimization through the lens of machine learning theory. We provide generalization guarantees on selecting parameters for multi-objective optimization algorithms based on sampled problem instances. Moreover, if the performance metric of the algorithm is the Pareto volume, we can PAC-learn the approximately optimal configuration in polynomial time. We apply our framework to various algorithms, including approximation algorithms, local search, and linear programming. Experiments on multiple problems verify our theoretical findings.} }
Endnote
%0 Conference Paper %T Learning Configurations for Data-Driven Multi-Objective Optimization %A Zhiyang Chen %A Hailong Yao %A Xia Yin %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-chen25ce %I PMLR %P 9642--9663 %U https://proceedings.mlr.press/v267/chen25ce.html %V 267 %X Multi-objective optimization problems arise widely in various fields. In practice, multi-objective optimization is generally solved by heuristics with tunable parameters that are highly application-specific. Tuning parameters based on real-world instances (a.k.a. algorithm configuration) are generally empirical without theoretical guarantees. In this work, we establish the theoretical foundation of data-driven multi-objective optimization through the lens of machine learning theory. We provide generalization guarantees on selecting parameters for multi-objective optimization algorithms based on sampled problem instances. Moreover, if the performance metric of the algorithm is the Pareto volume, we can PAC-learn the approximately optimal configuration in polynomial time. We apply our framework to various algorithms, including approximation algorithms, local search, and linear programming. Experiments on multiple problems verify our theoretical findings.
APA
Chen, Z., Yao, H. & Yin, X.. (2025). Learning Configurations for Data-Driven Multi-Objective Optimization. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:9642-9663 Available from https://proceedings.mlr.press/v267/chen25ce.html.

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