Efficient First-Order Optimization on the Pareto Set for Multi-Objective Learning under Preference Guidance
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913775562522624 |
|---|---|
| author | Chen, Lisha Xiao, Quan Fukuda, Ellen Hidemi Chen, Xinyi Yuan, Kun Chen, Tianyi |
| author_facet | Chen, Lisha Xiao, Quan Fukuda, Ellen Hidemi Chen, Xinyi Yuan, Kun Chen, Tianyi |
| contents | Multi-objective learning under user-specified preference is common in real-world problems such as multi-lingual speech recognition under fairness. In this work, we frame such a problem as a semivectorial bilevel optimization problem, whose goal is to optimize a pre-defined preference function, subject to the constraint that the model parameters are weakly Pareto optimal. To solve this problem, we convert the multi-objective constraints to a single-objective constraint through a merit function with an easy-to-evaluate gradient, and then, we use a penalty-based reformulation of the bilevel optimization problem. We theoretically establish the properties of the merit function, and the relations of solutions for the penalty reformulation and the constrained formulation. Then we propose algorithms to solve the reformulated single-level problem, and establish its convergence guarantees. We test the method on various synthetic and real-world problems. The results demonstrate the effectiveness of the proposed method in finding preference-guided optimal solutions to the multi-objective problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02854 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient First-Order Optimization on the Pareto Set for Multi-Objective Learning under Preference Guidance Chen, Lisha Xiao, Quan Fukuda, Ellen Hidemi Chen, Xinyi Yuan, Kun Chen, Tianyi Optimization and Control Machine Learning Multi-objective learning under user-specified preference is common in real-world problems such as multi-lingual speech recognition under fairness. In this work, we frame such a problem as a semivectorial bilevel optimization problem, whose goal is to optimize a pre-defined preference function, subject to the constraint that the model parameters are weakly Pareto optimal. To solve this problem, we convert the multi-objective constraints to a single-objective constraint through a merit function with an easy-to-evaluate gradient, and then, we use a penalty-based reformulation of the bilevel optimization problem. We theoretically establish the properties of the merit function, and the relations of solutions for the penalty reformulation and the constrained formulation. Then we propose algorithms to solve the reformulated single-level problem, and establish its convergence guarantees. We test the method on various synthetic and real-world problems. The results demonstrate the effectiveness of the proposed method in finding preference-guided optimal solutions to the multi-objective problem. |
| title | Efficient First-Order Optimization on the Pareto Set for Multi-Objective Learning under Preference Guidance |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2504.02854 |