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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.19377 |
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| _version_ | 1866916758489661440 |
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| author | Mielke, Arman Bauknecht, Uwe Strauss, Thilo Niepert, Mathias |
| author_facet | Mielke, Arman Bauknecht, Uwe Strauss, Thilo Niepert, Mathias |
| contents | Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing. While exact solutions are often computationally infeasible, many practical applications require high-quality solutions within a given time budget. To address this, we propose a learning-based approach that enhances existing non-learned approximation algorithms for CO. Specifically, we parameterize these approximation algorithms and train graph neural networks (GNNs) to predict parameter values that yield near-optimal solutions. Our method is trained end-to-end in a self-supervised fashion, using a novel gradient estimation scheme that treats the approximation algorithm as a black box. This approach combines the strengths of learning and traditional algorithms: the GNN learns from data to guide the algorithm toward better solutions, while the approximation algorithm ensures feasibility. We validate our method on two well-known combinatorial optimization problems: the travelling salesman problem (TSP) and the minimum k-cut problem. Our results demonstrate that the proposed approach is competitive with state-of-the-art learned CO solvers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19377 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Preference-Based Gradient Estimation for ML-Guided Approximate Combinatorial Optimization Mielke, Arman Bauknecht, Uwe Strauss, Thilo Niepert, Mathias Machine Learning Artificial Intelligence Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing. While exact solutions are often computationally infeasible, many practical applications require high-quality solutions within a given time budget. To address this, we propose a learning-based approach that enhances existing non-learned approximation algorithms for CO. Specifically, we parameterize these approximation algorithms and train graph neural networks (GNNs) to predict parameter values that yield near-optimal solutions. Our method is trained end-to-end in a self-supervised fashion, using a novel gradient estimation scheme that treats the approximation algorithm as a black box. This approach combines the strengths of learning and traditional algorithms: the GNN learns from data to guide the algorithm toward better solutions, while the approximation algorithm ensures feasibility. We validate our method on two well-known combinatorial optimization problems: the travelling salesman problem (TSP) and the minimum k-cut problem. Our results demonstrate that the proposed approach is competitive with state-of-the-art learned CO solvers. |
| title | Preference-Based Gradient Estimation for ML-Guided Approximate Combinatorial Optimization |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2502.19377 |