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.

翻译：机器学习能显著提升众多领域中不确定性决策的性能表现。然而，要确保稳健性保证，需要具备良好校准的不确定性估计，这对于深度神经网络等高容量预测模型而言往往难以实现。此外，在高维场景下，可能存在多种有效的不确定性估计方法，每种方法都具有其独特的性能特征——即并非所有不确定性对下游决策都具有同等价值。为解决这一问题，本文开发了一种端到端框架，用于学习条件稳健优化的不确定性估计，其稳健性与校准保证由保形预测提供。此外，我们提出使用部分输入凸神经网络表示任意凸不确定性集合，该网络将作为我们框架的组成部分进行学习。在能源存储套利和投资组合优化等具体应用中，我们的方法相较于两阶段“先估计后优化”基线模型展现出持续的性能提升。