Bundle Network: a Machine Learning-Based Bundle Method

• URL: http://arxiv.org/abs/2509.24736v1
• Date: Mon, 29 Sep 2025 12:59:49 GMT
• Title: Bundle Network: a Machine Learning-Based Bundle Method
• Authors: Francesca Demelas, Joseph Le Roux, Antonio Frangioni, Mathieu Lacroix, Emiliano Traversi, Roberto Wolfler Calvo,
• Abstract summary: This paper presents Bundle Network, a learning-based algorithm inspired by the Bundle Method for convex non-smooth problems.<n>By leveraging the unrolled graph of computation, our Bundle Network can be trained end-to-end via automatic differentiation.
• Score: 5.611428210450043
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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