Successful machine learning involves a complete pipeline of data, model, and downstream applications. Instead of treating them separately, there has been a prominent increase of attention within the constrained optimization (CO) and machine learning (ML) communities towards combining prediction and optimization models. The so-called end-to-end (E2E) learning captures the task-based objective for which they will be used for decision making. Although a large variety of E2E algorithms have been presented, it has not been fully investigated how to systematically address uncertainties involved in such models. Most of the existing work considers the uncertainties of ML in the input space and improves robustness through adversarial training. We apply the same idea to E2E learning and prove that there is a robustness certification procedure by solving augmented integer programming. Furthermore, we show that neglecting the uncertainty of COs during training causes a new trigger for generalization errors. To include all these components, we propose a unified framework that covers the uncertainties emerging in both the input feature space of the ML models and the COs. The framework is described as a robust optimization problem and is practically solved via end-to-end adversarial training (E2E-AT). Finally, the performance of E2E-AT is evaluated by a real-world end-to-end power system operation problem, including load forecasting and sequential scheduling tasks.

翻译：成功的机器学习涉及数据、模型与下游应用的完整流程。约束优化（CO）与机器学习（ML）领域的研究者不再将各环节独立处理，而是日益关注预测与优化模型的结合。所谓的端到端（E2E）学习能够捕捉用于决策的任务导向目标。尽管已有多种E2E算法被提出，但如何系统性地处理此类模型中涉及的不确定性尚未得到充分研究。现有工作大多关注ML在输入空间中的不确定性，并通过对抗训练提升鲁棒性。我们将相同思路应用于E2E学习，并证明通过求解增广整数规划可建立鲁棒性验证流程。进一步研究表明，训练过程中忽略CO的不确定性会引发新的泛化误差诱因。为综合这些要素，我们提出了一种统一框架，覆盖ML模型输入特征空间与CO中涌现的不确定性。该框架被形式化为鲁棒优化问题，并通过端到端对抗训练（E2E-AT）进行实际求解。最后，基于包含负荷预测与顺序调度任务的真实电力系统运行问题，验证了E2E-AT的性能。