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

arXiv: https://arxiv.org/abs/2312.10587 · HTML: https://mlsanity.com/paper/2312.10587/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 17 Dec 2023.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Adversarial Distributional Training for Robust Deep Learning](https://mlsanity.com/paper/2002.05999/) (2020)
- [Training for Faster Adversarial Robustness Verification via Inducing ReLU Stability](https://mlsanity.com/paper/1809.03008/) (2018)
- [Enforcing Policy Feasibility Constraints through Differentiable Projection for Energy Optimization](https://mlsanity.com/paper/2105.08881/) (2021)
- [End-to-End Stochastic Optimization with Energy-Based Model](https://mlsanity.com/paper/2211.13837/) (2022)
- [Adversarially Robust Learning for Security-Constrained Optimal Power Flow](https://mlsanity.com/paper/2111.06961/) (2021)
- [Robust Moving Target Defence Against False Data Injection Attacks in Power Grids](https://mlsanity.com/paper/2111.06346/) (2021)

## Built on by (most cited first, 2 of 2)

- [Learning-Augmented Power System Operations: A Unified Optimization View](https://mlsanity.com/paper/2505.05203/) (2025)
- [Decision-Focused Continual Learning for Seaport Power-Logistics Scheduling: Generalization across Varying Tasks](https://mlsanity.com/paper/2511.07938/) (2025)

## Abstract (arXiv)

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.