E2E-AT: A Unified Framework for Tackling Uncertainty in Task-aware End-to-end Learning

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.