Smooth Tchebycheff Scalarization for Multi-Objective Optimization

Xi Lin, Xiaoyuan Zhang, Zhiyuan Yang, Fei Liu, Zhenkun Wang, Qingfu Zhang
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:30479-30509, 2024.

Abstract

Multi-objective optimization problems can be found in many real-world applications, where the objectives often conflict each other and cannot be optimized by a single solution. In the past few decades, numerous methods have been proposed to find Pareto solutions that represent optimal trade-offs among the objectives for a given problem. However, these existing methods could have high computational complexity or may not have good theoretical properties for solving a general differentiable multi-objective optimization problem. In this work, by leveraging the smooth optimization technique, we propose a lightweight and efficient smooth Tchebycheff scalarization approach for gradient-based multi-objective optimization. It has good theoretical properties for finding all Pareto solutions with valid trade-off preferences, while enjoying significantly lower computational complexity compared to other methods. Experimental results on various real-world application problems fully demonstrate the effectiveness of our proposed method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-lin24y, title = {Smooth Tchebycheff Scalarization for Multi-Objective Optimization}, author = {Lin, Xi and Zhang, Xiaoyuan and Yang, Zhiyuan and Liu, Fei and Wang, Zhenkun and Zhang, Qingfu}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {30479--30509}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/lin24y/lin24y.pdf}, url = {https://proceedings.mlr.press/v235/lin24y.html}, abstract = {Multi-objective optimization problems can be found in many real-world applications, where the objectives often conflict each other and cannot be optimized by a single solution. In the past few decades, numerous methods have been proposed to find Pareto solutions that represent optimal trade-offs among the objectives for a given problem. However, these existing methods could have high computational complexity or may not have good theoretical properties for solving a general differentiable multi-objective optimization problem. In this work, by leveraging the smooth optimization technique, we propose a lightweight and efficient smooth Tchebycheff scalarization approach for gradient-based multi-objective optimization. It has good theoretical properties for finding all Pareto solutions with valid trade-off preferences, while enjoying significantly lower computational complexity compared to other methods. Experimental results on various real-world application problems fully demonstrate the effectiveness of our proposed method.} }
Endnote
%0 Conference Paper %T Smooth Tchebycheff Scalarization for Multi-Objective Optimization %A Xi Lin %A Xiaoyuan Zhang %A Zhiyuan Yang %A Fei Liu %A Zhenkun Wang %A Qingfu Zhang %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-lin24y %I PMLR %P 30479--30509 %U https://proceedings.mlr.press/v235/lin24y.html %V 235 %X Multi-objective optimization problems can be found in many real-world applications, where the objectives often conflict each other and cannot be optimized by a single solution. In the past few decades, numerous methods have been proposed to find Pareto solutions that represent optimal trade-offs among the objectives for a given problem. However, these existing methods could have high computational complexity or may not have good theoretical properties for solving a general differentiable multi-objective optimization problem. In this work, by leveraging the smooth optimization technique, we propose a lightweight and efficient smooth Tchebycheff scalarization approach for gradient-based multi-objective optimization. It has good theoretical properties for finding all Pareto solutions with valid trade-off preferences, while enjoying significantly lower computational complexity compared to other methods. Experimental results on various real-world application problems fully demonstrate the effectiveness of our proposed method.
APA
Lin, X., Zhang, X., Yang, Z., Liu, F., Wang, Z. & Zhang, Q.. (2024). Smooth Tchebycheff Scalarization for Multi-Objective Optimization. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:30479-30509 Available from https://proceedings.mlr.press/v235/lin24y.html.

Related Material