On the Effectiveness of Classical Regression Methods for Optimal Switching Problems
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910092023037952 |
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| author | Andersson, Martin Avelin, Benny Olofsson, Marcus |
| author_facet | Andersson, Martin Avelin, Benny Olofsson, Marcus |
| contents | Simple regression methods provide robust, near-optimal solutions for optimal switching problems, including high-dimensional ones (up to 50). While the theory requires solving intractable PDE systems, the Longstaff-Schwartz algorithm with classical regression methods achieves excellent switching decisions without extensive hyperparameter tuning. Testing linear models (OLS, Ridge, LASSO), tree-based methods (random forests, gradient boosting), $k$-nearest neighbors, and feedforward neural networks on four benchmark problems, we find that several simple methods maintain stable performance across diverse problem characteristics, outperforming the neural networks we tested against. In our comparison, $k$-NN regression performs consistently well, and with minimal hyperparameter tuning. We establish concentration bounds for this regressor and show that PCA enables $k$-NN to scale to high dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15436 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Effectiveness of Classical Regression Methods for Optimal Switching Problems Andersson, Martin Avelin, Benny Olofsson, Marcus Optimization and Control Statistics Theory Simple regression methods provide robust, near-optimal solutions for optimal switching problems, including high-dimensional ones (up to 50). While the theory requires solving intractable PDE systems, the Longstaff-Schwartz algorithm with classical regression methods achieves excellent switching decisions without extensive hyperparameter tuning. Testing linear models (OLS, Ridge, LASSO), tree-based methods (random forests, gradient boosting), $k$-nearest neighbors, and feedforward neural networks on four benchmark problems, we find that several simple methods maintain stable performance across diverse problem characteristics, outperforming the neural networks we tested against. In our comparison, $k$-NN regression performs consistently well, and with minimal hyperparameter tuning. We establish concentration bounds for this regressor and show that PCA enables $k$-NN to scale to high dimensions. |
| title | On the Effectiveness of Classical Regression Methods for Optimal Switching Problems |
| topic | Optimization and Control Statistics Theory |
| url | https://arxiv.org/abs/2506.15436 |