From Data to Uncertainty Sets: a Machine Learning Approach
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916642407055360 |
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| author | Bertsimas, Dimitris Boucher, Benjamin |
| author_facet | Bertsimas, Dimitris Boucher, Benjamin |
| contents | Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However, when applied to uncertain constraints, these methods rarely work because satisfying a crucial constraint in expectation may result in a high probability of violation. To remedy this, we leverage robust optimization to protect a constraint against the uncertainty of a machine learning model's output. To do so, we design an uncertainty set based on the model's loss function. Intuitively, this approach attempts to minimize the uncertainty around a prediction. Extending guarantees from the robust optimization literature, we derive strong guarantees on the probability of violation. On synthetic computational experiments, our method requires uncertainty sets with radii up to one order of magnitude smaller than those of other approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02173 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Data to Uncertainty Sets: a Machine Learning Approach Bertsimas, Dimitris Boucher, Benjamin Machine Learning Optimization and Control Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However, when applied to uncertain constraints, these methods rarely work because satisfying a crucial constraint in expectation may result in a high probability of violation. To remedy this, we leverage robust optimization to protect a constraint against the uncertainty of a machine learning model's output. To do so, we design an uncertainty set based on the model's loss function. Intuitively, this approach attempts to minimize the uncertainty around a prediction. Extending guarantees from the robust optimization literature, we derive strong guarantees on the probability of violation. On synthetic computational experiments, our method requires uncertainty sets with radii up to one order of magnitude smaller than those of other approaches. |
| title | From Data to Uncertainty Sets: a Machine Learning Approach |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2503.02173 |