  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 extend
this 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.
