A Primal-Dual-Assisted Penalty Approach to Bilevel Optimization with Coupled Constraints
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909295585525760 |
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| author | Jiang, Liuyuan Xiao, Quan Tenorio, Victor M. Real-Rojas, Fernando Marques, Antonio G. Chen, Tianyi |
| author_facet | Jiang, Liuyuan Xiao, Quan Tenorio, Victor M. Real-Rojas, Fernando Marques, Antonio G. Chen, Tianyi |
| contents | Interest in bilevel optimization has grown in recent years, partially due to its applications to tackle challenging machine-learning problems. Several exciting recent works have been centered around developing efficient gradient-based algorithms that can solve bilevel optimization problems with provable guarantees. However, the existing literature mainly focuses on bilevel problems either without constraints, or featuring only simple constraints that do not couple variables across the upper and lower levels, excluding a range of complex applications. Our paper studies this challenging but less explored scenario and develops a (fully) first-order algorithm, which we term BLOCC, to tackle BiLevel Optimization problems with Coupled Constraints. We establish rigorous convergence theory for the proposed algorithm and demonstrate its effectiveness on two well-known real-world applications - hyperparameter selection in support vector machine (SVM) and infrastructure planning in transportation networks using the real data from the city of Seville. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10148 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Primal-Dual-Assisted Penalty Approach to Bilevel Optimization with Coupled Constraints Jiang, Liuyuan Xiao, Quan Tenorio, Victor M. Real-Rojas, Fernando Marques, Antonio G. Chen, Tianyi Optimization and Control Machine Learning Interest in bilevel optimization has grown in recent years, partially due to its applications to tackle challenging machine-learning problems. Several exciting recent works have been centered around developing efficient gradient-based algorithms that can solve bilevel optimization problems with provable guarantees. However, the existing literature mainly focuses on bilevel problems either without constraints, or featuring only simple constraints that do not couple variables across the upper and lower levels, excluding a range of complex applications. Our paper studies this challenging but less explored scenario and develops a (fully) first-order algorithm, which we term BLOCC, to tackle BiLevel Optimization problems with Coupled Constraints. We establish rigorous convergence theory for the proposed algorithm and demonstrate its effectiveness on two well-known real-world applications - hyperparameter selection in support vector machine (SVM) and infrastructure planning in transportation networks using the real data from the city of Seville. |
| title | A Primal-Dual-Assisted Penalty Approach to Bilevel Optimization with Coupled Constraints |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2406.10148 |