{"ID":2863582,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.24736","arxiv_id":"2509.24736","title":"Bundle Network: a Machine Learning-Based Bundle Method","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2509.24736","url_pdf":"https://arxiv.org/pdf/2509.24736v1","authors":"[\"Francesca Demelas\",\"Joseph Le Roux\",\"Antonio Frangioni\",\"Mathieu Lacroix\",\"Emiliano Traversi\",\"Roberto Wolfler Calvo\"]","published":"2025-09-29T12:59:49Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"cs.LG\"]","methods":"[]","has_code":false}