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.

本研究针对高容量预测模型中校准不确定性估计的困难，开发了一种端到端框架以学习条件鲁棒优化的不确定性估计，并通过符合性预测提供鲁棒性和校准保证。该方法在能量存储套利和投资组合优化的具体应用中，表现出持续优于两阶段估计-再优化基线的方法。 

端到端的符合性校准用于不确定性下的优化