Pinet: Optimizing hard-constrained neural networks with orthogonal projection layers
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911452700344320 |
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| author | Grontas, Panagiotis D. Terpin, Antonio Balta, Efe C. D'Andrea, Raffaello Lygeros, John |
| author_facet | Grontas, Panagiotis D. Terpin, Antonio Balta, Efe C. D'Andrea, Raffaello Lygeros, John |
| contents | We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $Π$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem for backpropagation. We deploy $Π$net as a feasible-by-design optimization proxy for parametric constrained optimization problems and obtain modest-accuracy solutions faster than traditional solvers when solving a single problem, and significantly faster for a batch of problems. We surpass state-of-the-art learning approaches by orders of magnitude in terms of training time, solution quality, and robustness to hyperparameter tuning, while maintaining similar inference times. Finally, we tackle multi-vehicle motion planning with non-convex trajectory preferences and provide $Π$net as a GPU-ready package implemented in JAX. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10480 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pinet: Optimizing hard-constrained neural networks with orthogonal projection layers Grontas, Panagiotis D. Terpin, Antonio Balta, Efe C. D'Andrea, Raffaello Lygeros, John Machine Learning Artificial Intelligence Optimization and Control We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $Π$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem for backpropagation. We deploy $Π$net as a feasible-by-design optimization proxy for parametric constrained optimization problems and obtain modest-accuracy solutions faster than traditional solvers when solving a single problem, and significantly faster for a batch of problems. We surpass state-of-the-art learning approaches by orders of magnitude in terms of training time, solution quality, and robustness to hyperparameter tuning, while maintaining similar inference times. Finally, we tackle multi-vehicle motion planning with non-convex trajectory preferences and provide $Π$net as a GPU-ready package implemented in JAX. |
| title | Pinet: Optimizing hard-constrained neural networks with orthogonal projection layers |
| topic | Machine Learning Artificial Intelligence Optimization and Control |
| url | https://arxiv.org/abs/2508.10480 |