A Hybrid Learning-to-Optimize Framework for Mixed-Integer Quadratic Programming
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909038698037248 |
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| author | Le, Viet-Anh Xie, Mu Mangharam, Rahul |
| author_facet | Le, Viet-Anh Xie, Mu Mangharam, Rahul |
| contents | In this paper, we propose a learning-to-optimize (L2O) framework to accelerate solving parametric mixed-integer quadratic programming (MIQP) problems, with a particular focus on mixed-integer model predictive control (MI-MPC) applications. The framework learns to predict integer solutions with enhanced optimality and feasibility by integrating supervised learning (for optimality), self-supervised learning (for feasibility), and a differentiable quadratic programming (QP) layer, resulting in a hybrid L2O framework. Specifically, a neural network (NN) is used to learn the mapping from problem parameters to optimal integer solutions, while a differentiable QP layer is integrated to compute the corresponding continuous variables given the predicted integers and problem parameters. Moreover, a hybrid loss function is proposed, which combines a supervised loss with respect to the global optimal solution, and a self-supervised loss derived from the problem's objective and constraints. The effectiveness of the proposed framework is demonstrated on two benchmark MI-MPC problems, with comparative results against purely supervised and self-supervised learning models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19383 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Hybrid Learning-to-Optimize Framework for Mixed-Integer Quadratic Programming Le, Viet-Anh Xie, Mu Mangharam, Rahul Systems and Control In this paper, we propose a learning-to-optimize (L2O) framework to accelerate solving parametric mixed-integer quadratic programming (MIQP) problems, with a particular focus on mixed-integer model predictive control (MI-MPC) applications. The framework learns to predict integer solutions with enhanced optimality and feasibility by integrating supervised learning (for optimality), self-supervised learning (for feasibility), and a differentiable quadratic programming (QP) layer, resulting in a hybrid L2O framework. Specifically, a neural network (NN) is used to learn the mapping from problem parameters to optimal integer solutions, while a differentiable QP layer is integrated to compute the corresponding continuous variables given the predicted integers and problem parameters. Moreover, a hybrid loss function is proposed, which combines a supervised loss with respect to the global optimal solution, and a self-supervised loss derived from the problem's objective and constraints. The effectiveness of the proposed framework is demonstrated on two benchmark MI-MPC problems, with comparative results against purely supervised and self-supervised learning models. |
| title | A Hybrid Learning-to-Optimize Framework for Mixed-Integer Quadratic Programming |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2511.19383 |