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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.16826 |
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| _version_ | 1866912228045750272 |
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| author | Jiménez, Diego Pagnoncelli, Bernardo K. Yaman, Hande |
| author_facet | Jiménez, Diego Pagnoncelli, Bernardo K. Yaman, Hande |
| contents | The recent interest in contextual optimization problems, where randomness is associated with side information, has led to two primary strategies for formulation and solution. The first, estimate-then-optimize, separates the estimation of the problem's parameters from the optimization process. The second, decision-focused optimization, integrates the optimization problem's structure directly into the prediction procedure. In this work, we propose a pessimistic bilevel approach for solving general decision-focused formulations of combinatorial optimization problems. Our method solves an $\varepsilon$-approximation of the pessimistic bilevel problem using a specialized cut generation algorithm. We benchmark its performance on the 0-1 knapsack problem against estimate-then-optimize and decision-focused methods, including the popular SPO+ approach. Computational experiments highlight the proposed method's advantages, particularly in reducing out-of-sample regret. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16826 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pessimistic bilevel optimization approach for decision-focused learning Jiménez, Diego Pagnoncelli, Bernardo K. Yaman, Hande Optimization and Control Discrete Mathematics 90B99 The recent interest in contextual optimization problems, where randomness is associated with side information, has led to two primary strategies for formulation and solution. The first, estimate-then-optimize, separates the estimation of the problem's parameters from the optimization process. The second, decision-focused optimization, integrates the optimization problem's structure directly into the prediction procedure. In this work, we propose a pessimistic bilevel approach for solving general decision-focused formulations of combinatorial optimization problems. Our method solves an $\varepsilon$-approximation of the pessimistic bilevel problem using a specialized cut generation algorithm. We benchmark its performance on the 0-1 knapsack problem against estimate-then-optimize and decision-focused methods, including the popular SPO+ approach. Computational experiments highlight the proposed method's advantages, particularly in reducing out-of-sample regret. |
| title | Pessimistic bilevel optimization approach for decision-focused learning |
| topic | Optimization and Control Discrete Mathematics 90B99 |
| url | https://arxiv.org/abs/2501.16826 |