The field of Contextual Optimization (CO) integrates machine learning and optimization to solve decision making problems under uncertainty. Recently, a risk sensitive variant of CO, known as Conditional Robust Optimization (CRO), combines uncertainty quantification with robust optimization in order to promote safety and reliability in high stake applications. Exploiting modern differentiable optimization methods, we propose a novel end-to-end approach to train a CRO model in a way that accounts for both the empirical risk of the prescribed decisions and the quality of conditional coverage of the contextual uncertainty set that supports them. While guarantees of success for the latter objective are impossible to obtain from the point of view of conformal prediction theory, high quality conditional coverage is achieved empirically by ingeniously employing a logistic regression differentiable layer within the calculation of coverage quality in our training loss. We show that the proposed training algorithms produce decisions that outperform the traditional estimate then optimize approaches.

翻译：条件优化（CO）领域融合了机器学习与优化方法以解决不确定性下的决策问题。最近，作为条件优化的风险敏感变体，条件鲁棒优化（CRO）将不确定性量化与鲁棒优化相结合，旨在提升高风险应用场景中的安全性与可靠性。通过利用现代可微优化方法，我们提出了一种新颖的端到端方法训练CRO模型，该方法同时兼顾决策方案的实证风险及其所依赖的条件不确定性集合的覆盖质量。虽然从保形预测理论角度无法保证后一目标的成功实现，但我们通过巧妙地在训练损失函数中引入逻辑回归可微层来计算覆盖质量，从而在实证层面实现了高质量的条件覆盖。实验证明，所提出的训练算法生成的决策方案优于传统"先估计后优化"的方法。