Bundle Network: a Machine Learning-Based Bundle Method
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918150579159040 |
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| author | Demelas, Francesca Roux, Joseph Le Frangioni, Antonio Lacroix, Mathieu Traversi, Emiliano Calvo, Roberto Wolfler |
| author_facet | Demelas, Francesca Roux, Joseph Le Frangioni, Antonio Lacroix, Mathieu Traversi, Emiliano Calvo, Roberto Wolfler |
| contents | This paper presents Bundle Network, a learning-based algorithm inspired by the Bundle Method for convex non-smooth minimization problems. Unlike classical approaches that rely on heuristic tuning of a regularization parameter, our method automatically learns to adjust it from data. Furthermore, we replace the iterative resolution of the optimization problem that provides the search direction-traditionally computed as a convex combination of gradients at visited points-with a recurrent neural model equipped with an attention mechanism. By leveraging the unrolled graph of computation, our Bundle Network can be trained end-to-end via automatic differentiation. Experiments on Lagrangian dual relaxations of the Multi-Commodity Network Design and Generalized Assignment problems demonstrate that our approach consistently outperforms traditional methods relying on grid search for parameter tuning, while generalizing effectively across datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24736 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bundle Network: a Machine Learning-Based Bundle Method Demelas, Francesca Roux, Joseph Le Frangioni, Antonio Lacroix, Mathieu Traversi, Emiliano Calvo, Roberto Wolfler Optimization and Control Machine Learning This paper presents Bundle Network, a learning-based algorithm inspired by the Bundle Method for convex non-smooth minimization problems. Unlike classical approaches that rely on heuristic tuning of a regularization parameter, our method automatically learns to adjust it from data. Furthermore, we replace the iterative resolution of the optimization problem that provides the search direction-traditionally computed as a convex combination of gradients at visited points-with a recurrent neural model equipped with an attention mechanism. By leveraging the unrolled graph of computation, our Bundle Network can be trained end-to-end via automatic differentiation. Experiments on Lagrangian dual relaxations of the Multi-Commodity Network Design and Generalized Assignment problems demonstrate that our approach consistently outperforms traditional methods relying on grid search for parameter tuning, while generalizing effectively across datasets. |
| title | Bundle Network: a Machine Learning-Based Bundle Method |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2509.24736 |