# Learning Decision-Focused Uncertainty Sets in Robust Optimization

arXiv: https://arxiv.org/abs/2305.19225 · HTML: https://mlsanity.com/paper/2305.19225/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2023.

## Built on by (most cited first, 13 of 13)

- [Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents](https://mlsanity.com/paper/2502.02561/) (2025)
- [End-to-End Conformal Calibration for Optimization Under Uncertainty](https://mlsanity.com/paper/2409.20534/) (2024)
- [Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints](https://mlsanity.com/paper/2505.22881/) (2025)
- [Decision-calibrated prediction sets for robust power system operations](https://mlsanity.com/paper/2606.02081/) (2026)
- [Conformal Risk-Averse Decision Making with Action Conditional Guarantee](https://mlsanity.com/paper/2606.05551/) (2026)
- [Self-Supervised Penalty-Based Learning for Robust Constrained Optimization](https://mlsanity.com/paper/2503.05175/) (2025)
- [Distributionally Robust Control with End-to-End Statistically Guaranteed Metric Learning](https://mlsanity.com/paper/2510.10214/) (2025)
- [Worst-Case Distance-Aware Error Bounds for Neural Networks](https://mlsanity.com/paper/2510.22021/) (2025)
- [Learning Predictive Ambiguity Sets for Decision-Focused Distributionally Robust Optimization](https://mlsanity.com/paper/2607.09820/) (2026)
- [Generative Distributionally Robust Optimization](https://mlsanity.com/paper/2607.24983/) (2026)
- [The Value of Human Expertise](https://mlsanity.com/paper/2608.26051/) (2026)
- [Decision-Focused Learning in MDPs: An Occupancy Measure Approach](https://mlsanity.com/paper/2610.08384/) (2026)
- [Calibrating Ambiguity Set via Diagnostic Transport for Distributionally Robust Optimization](https://mlsanity.com/paper/2610.10793/) (2026)

## Abstract (arXiv)

We propose a data-driven technique to automatically learn contextual uncertainty sets in robust optimization, resulting in excellent worst-case and average-case performance while also guaranteeing constraint satisfaction. Our method reshapes the uncertainty sets by minimizing the expected performance across a contextual family of problems, subject to conditional-value-at-risk constraints. Our approach is very flexible, and can learn a wide variety of uncertainty sets while preserving tractability. We solve the constrained learning problem using a stochastic augmented Lagrangian method that relies on differentiating the solutions of the robust optimization problems with respect to the parameters of the uncertainty set. Due to the nonsmooth and nonconvex nature of the augmented Lagrangian function, we apply the nonsmooth conservative implicit function theorem to establish convergence to a critical point, which is a feasible solution of the constrained problem under mild assumptions. Using empirical process theory, we show finite-sample probabilistic guarantees of constraint satisfaction for the resulting solutions. Numerical experiments show that our method outperforms traditional approaches in robust and distributionally robust optimization in terms of out-of-sample performance and constraint satisfaction guarantees.