End-to-End Conformal Calibration for Optimization Under Uncertainty

• URL: http://arxiv.org/abs/2409.20534v1
• Date: Mon, 30 Sep 2024 17:38:27 GMT
• Title: End-to-End Conformal Calibration for Optimization Under Uncertainty
• Authors: Christopher Yeh, Nicolas Christianson, Alan Wu, Adam Wierman, Yisong Yue,
• Abstract summary: This paper develops an end-to-end framework to learn the uncertainty estimates for conditional optimization. In addition, we propose to represent arbitrary convex uncertainty sets with partially convex neural networks. Our approach consistently improves upon two-stage-then-optimize.
• Score: 32.844953018302874
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Machine learning can significantly improve performance for decision-making under uncertainty in a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to achieve in high-capacity prediction models such as deep neural networks. Moreover, in high-dimensional settings, there may be many valid uncertainty estimates, each with their 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 the uncertainty estimates for conditional robust optimization, with robustness and calibration guarantees provided by conformal prediction. In addition, we propose to represent arbitrary 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.

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