# Decision-calibrated prediction sets for robust power system operations

arXiv: https://arxiv.org/abs/2606.02081 · HTML: https://mlsanity.com/paper/2606.02081/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 52 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Builds on (most cited first, 23 of 23)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [Non-Exchangeable Conformal Risk Control](https://mlsanity.com/paper/2310.01262/) (2023)
- [Minimum Volume Conformal Sets for Multivariate Regression](https://mlsanity.com/paper/2503.19068/) (2025)
- [Distributionally robust stochastic programs with side information based on trimmings -- Extended version](https://mlsanity.com/paper/2009.10592/) (2020)
- [End-to-end Conditional Robust Optimization](https://mlsanity.com/paper/2403.04670/) (2024)
- [End-to-End Conformal Calibration for Optimization Under Uncertainty](https://mlsanity.com/paper/2409.20534/) (2024)
- [Learning Decision-Focused Uncertainty Sets in Robust Optimization](https://mlsanity.com/paper/2305.19225/) (2023)
- [Conformal Risk Training: End-to-End Optimization of Conformal Risk Control](https://mlsanity.com/paper/2510.08748/) (2025)
- [Learning-based Robust Optimization: Procedures and Statistical Guarantees](https://mlsanity.com/paper/1704.04342/) (2017)
- [Weather-Informed Probabilistic Forecasting and Scenario Generation in Power Systems](https://mlsanity.com/paper/2409.07637/) (2024)
- [Predict-and-Optimize Robust Unit Commitment with Statistical Guarantees via Weight Combination](https://mlsanity.com/paper/2411.03138/) (2024)
- [Learning Data-Driven Uncertainty Set Partitions for Robust and Adaptive Energy Forecasting with Missing Data](https://mlsanity.com/paper/2503.20410/) (2025)
- [Enhancing Electricity-System Resilience with Adaptive Robust Optimization and Conformal Uncertainty Characterization](https://mlsanity.com/paper/2505.11627/) (2025)
- [Scores for Multivariate Distributions and Level Sets](https://mlsanity.com/paper/2002.09578/) (2020)
- [Chance Constraint Tuning for Optimal Power Flow](https://mlsanity.com/paper/2005.13428/) (2020)
- [Prescribed Robustness in Optimal Power Flow](https://mlsanity.com/paper/2310.02957/) (2023)
- [A Conformal Prediction-Based Chance-Constrained Programming Approach for 24/7 Carbon-Free Data Center Operation Scheduling](https://mlsanity.com/paper/2510.04053/) (2025)
- [CoCopula: Conformal Calibration and Copula Aggregation for Reliable Renewable Energy Forecasting](https://mlsanity.com/paper/2602.02583/) (2026)
- [Constructing Deployment Scenarios for Reserve Deliverability via Adaptive Robust Optimization](https://mlsanity.com/paper/2603.16752/) (2026)

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

- [Audited Selective Verification for Risk-Controlled N-1 Thermal Contingency Screening under Deployment Shift](https://mlsanity.com/paper/2607.13221/) (2026)
- [Finite-Sample Probabilistic Safety Certification for AI-Based Grid-Edge Coordination](https://mlsanity.com/paper/2609.28182/) (2026)

## Abstract (arXiv)

Robust optimization offers a tractable approach to balance operating costs and reliability in power systems dominated by weather-dependent renewable uncertainty, but its performance depends critically on the uncertainty set. Standard data-driven approaches often calibrate uncertainty sets to attain predictive coverage, which can produce unnecessarily large sets and costly operating decisions. In contrast, we introduce decision-calibrated prediction sets and embed them as uncertainty sets in robust optimization problems; these are conditional multivariate prediction sets where calibration is defined in terms of the reliability of downstream decisions, rather than in terms of the coverage. First, we learn these conditional prediction sets as sub-level sets of norm-based score functions represented by partially input-convex neural networks, capturing contextual information and multivariate dependence while preserving convexity and tractability in downstream robust formulations. Second, inspired by conformal risk control, we calibrate a score-threshold parameter that sets the volume of the uncertainty set, thereby controlling the expected violations of downstream operational constraints. We apply our approach to 15-minute-ahead reserve scheduling with network-constrained deliverability, which we formulate as a robust DC optimal power flow problem with affine recourse. Numerical experiments show that decision-calibrated sets attain prescribed constraint-satisfaction targets within about three percentage points, whereas standard coverage-based calibration systematically exceeds these targets by more than eleven percentage points, leading to larger sets and higher operating costs.