Optimization over Trained Neural Networks: Going Large with Gradient-Based Algorithms
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910056941879296 |
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| author | Tong, Jiatai Zhu, Yilin Serra, Thiago Burer, Samuel |
| author_facet | Tong, Jiatai Zhu, Yilin Serra, Thiago Burer, Samuel |
| contents | When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local search that exploits the neural-network structure has been employed to find good solutions within a reasonable time limit. For such methods, a lower per-iteration cost is advantageous when solving larger models. The contribution of this paper is two-fold. First, we propose a gradient-based algorithm with lower per-iteration cost than existing methods. Second, we further adapt this algorithm to exploit the piecewise-linear structure of neural networks that use Rectified Linear Units (ReLUs). In line with prior research, our methods become competitive with -- and then dominant over -- other local search methods as the optimization models become larger. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24295 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimization over Trained Neural Networks: Going Large with Gradient-Based Algorithms Tong, Jiatai Zhu, Yilin Serra, Thiago Burer, Samuel Optimization and Control When optimizing a nonlinear objective, one can employ a neural network as a surrogate for the nonlinear function. However, the resulting optimization model can be time-consuming to solve globally with exact methods. As a result, local search that exploits the neural-network structure has been employed to find good solutions within a reasonable time limit. For such methods, a lower per-iteration cost is advantageous when solving larger models. The contribution of this paper is two-fold. First, we propose a gradient-based algorithm with lower per-iteration cost than existing methods. Second, we further adapt this algorithm to exploit the piecewise-linear structure of neural networks that use Rectified Linear Units (ReLUs). In line with prior research, our methods become competitive with -- and then dominant over -- other local search methods as the optimization models become larger. |
| title | Optimization over Trained Neural Networks: Going Large with Gradient-Based Algorithms |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2512.24295 |