End-to-End Conformal Calibration for Optimization Under Uncertainty
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908803486711808 |
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| author | Yeh, Christopher Christianson, Nicolas Wu, Alan Wierman, Adam Yue, Yisong |
| author_facet | Yeh, Christopher Christianson, Nicolas Wu, Alan Wierman, Adam Yue, Yisong |
| contents | Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to achieve with neural networks. Moreover, in high-dimensional settings, there may be many valid uncertainty estimates, each with its own performance profile - i.e., not all uncertainty is equally valuable for downstream decision-making. To address this problem, this paper develops an end-to-end framework to learn uncertainty sets for conditional robust optimization in a way that is informed by the downstream decision-making loss, with robustness and calibration guarantees provided by conformal prediction. In addition, we propose to represent general convex uncertainty sets with partially input-convex neural networks, which are learned as part of our framework. Our approach consistently improves upon two-stage estimate-then-optimize baselines on concrete applications in energy storage arbitrage and portfolio optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20534 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | End-to-End Conformal Calibration for Optimization Under Uncertainty Yeh, Christopher Christianson, Nicolas Wu, Alan Wierman, Adam Yue, Yisong Machine Learning Optimization and Control Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to achieve with neural networks. Moreover, in high-dimensional settings, there may be many valid uncertainty estimates, each with its own performance profile - i.e., not all uncertainty is equally valuable for downstream decision-making. To address this problem, this paper develops an end-to-end framework to learn uncertainty sets for conditional robust optimization in a way that is informed by the downstream decision-making loss, with robustness and calibration guarantees provided by conformal prediction. In addition, we propose to represent general convex uncertainty sets with partially input-convex neural networks, which are learned as part of our framework. Our approach consistently improves upon two-stage estimate-then-optimize baselines on concrete applications in energy storage arbitrage and portfolio optimization. |
| title | End-to-End Conformal Calibration for Optimization Under Uncertainty |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2409.20534 |