Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2504.02833 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916673442807808 |
|---|---|
| author | Park, Sangwoo Vlaski, Stefan Hanzo, Lajos |
| author_facet | Park, Sangwoo Vlaski, Stefan Hanzo, Lajos |
| contents | In multi-objective optimization, minimizing the worst objective can be preferable to minimizing the average objective, as this ensures improved fairness across objectives. Due to the non-smooth nature of the resultant min-max optimization problem, classical subgradient-based approaches typically exhibit slow convergence. Motivated by primal-dual consensus techniques in multi-agent optimization and learning, we formulate a smooth variant of the min-max problem based on the augmented Lagrangian. The resultant Exact Pareto Optimization via Augmented Lagrangian (EPO-AL) algorithm scales better with the number of objectives than subgradient-based strategies, while exhibiting lower per-iteration complexity than recent smoothing-based counterparts. We establish that every fixed-point of the proposed algorithm is both Pareto and min-max optimal under mild assumptions and demonstrate its effectiveness in numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02833 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalable Min-Max Optimization via Primal-Dual Exact Pareto Optimization Park, Sangwoo Vlaski, Stefan Hanzo, Lajos Optimization and Control Machine Learning In multi-objective optimization, minimizing the worst objective can be preferable to minimizing the average objective, as this ensures improved fairness across objectives. Due to the non-smooth nature of the resultant min-max optimization problem, classical subgradient-based approaches typically exhibit slow convergence. Motivated by primal-dual consensus techniques in multi-agent optimization and learning, we formulate a smooth variant of the min-max problem based on the augmented Lagrangian. The resultant Exact Pareto Optimization via Augmented Lagrangian (EPO-AL) algorithm scales better with the number of objectives than subgradient-based strategies, while exhibiting lower per-iteration complexity than recent smoothing-based counterparts. We establish that every fixed-point of the proposed algorithm is both Pareto and min-max optimal under mild assumptions and demonstrate its effectiveness in numerical simulations. |
| title | Scalable Min-Max Optimization via Primal-Dual Exact Pareto Optimization |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2504.02833 |