Self-Supervised Learning of Iterative Solvers for Constrained Optimization
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912707877273600 |
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| author | Lüken, Lukas Lucia, Sergio |
| author_facet | Lüken, Lukas Lucia, Sergio |
| contents | The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control. To this end, this work presents a learning-based iterative solver for constrained optimization, comprising a neural network predictor that generates initial primal-dual solution estimates, followed by a learned iterative solver that refines these estimates to reach high accuracy. We introduce a novel loss function based on Karush-Kuhn-Tucker (KKT) optimality conditions, enabling fully self-supervised training without pre-sampled optimizer solutions. Theoretical guarantees ensure that the training loss function attains minima exclusively at KKT points. A convexification procedure enables application to nonconvex problems while preserving these guarantees. Experiments on two nonconvex case studies demonstrate speedups of up to one order of magnitude compared to state-of-the-art solvers such as IPOPT, while achieving orders of magnitude higher accuracy than competing learning-based approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08066 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-Supervised Learning of Iterative Solvers for Constrained Optimization Lüken, Lukas Lucia, Sergio Machine Learning Optimization and Control The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control. To this end, this work presents a learning-based iterative solver for constrained optimization, comprising a neural network predictor that generates initial primal-dual solution estimates, followed by a learned iterative solver that refines these estimates to reach high accuracy. We introduce a novel loss function based on Karush-Kuhn-Tucker (KKT) optimality conditions, enabling fully self-supervised training without pre-sampled optimizer solutions. Theoretical guarantees ensure that the training loss function attains minima exclusively at KKT points. A convexification procedure enables application to nonconvex problems while preserving these guarantees. Experiments on two nonconvex case studies demonstrate speedups of up to one order of magnitude compared to state-of-the-art solvers such as IPOPT, while achieving orders of magnitude higher accuracy than competing learning-based approaches. |
| title | Self-Supervised Learning of Iterative Solvers for Constrained Optimization |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2409.08066 |