# End-to-End Conformal Calibration for Optimization Under Uncertainty

arXiv: https://arxiv.org/abs/2409.20534 · HTML: https://mlsanity.com/paper/2409.20534/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 58 references that are in the map.
- First posted on arXiv 30 Sep 2024.

## Builds on (most cited first, 30 of 30)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Learning Optimal Conformal Classifiers](https://mlsanity.com/paper/2110.09192/) (2021)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [Optimal Control Via Neural Networks: A Convex Approach](https://mlsanity.com/paper/1805.11835/) (2018)
- [Uncertainty Baselines: Benchmarks for Uncertainty & Robustness in Deep Learning](https://mlsanity.com/paper/2106.04015/) (2021)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [Estimate-Then-Optimize versus Integrated-Estimation-Optimization versus Sample Average Approximation: A Stochastic Dominance Perspective](https://mlsanity.com/paper/2304.06833/) (2023)
- [Predict-then-Calibrate: A New Perspective of Robust Contextual LP](https://mlsanity.com/paper/2305.15686/) (2023)
- [End-to-end Conditional Robust Optimization](https://mlsanity.com/paper/2403.04670/) (2024)
- [Learning Decision-Focused Uncertainty Sets in Robust Optimization](https://mlsanity.com/paper/2305.19225/) (2023)
- [Disciplined Saddle Programming](https://mlsanity.com/paper/2301.13427/) (2023)
- [Wasserstein Distributionally Robust Look-Ahead Economic Dispatch](https://mlsanity.com/paper/2003.04874/) (2020)
- [On Well-Structured Convex-Concave Saddle Point Problems and Variational Inequalities with Monotone Operators](https://mlsanity.com/paper/2102.01002/) (2021)
- [A Chance-Constrained Stochastic Electricity Market](https://mlsanity.com/paper/1906.06963/) (2019)
- [Nonparametric Estimation of Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2004.03069/) (2020)

## Built on by (most cited first, 15 of 15)

- [Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents](https://mlsanity.com/paper/2502.02561/) (2025)
- [Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making](https://mlsanity.com/paper/2502.05468/) (2025)
- [Utility-Directed Conformal Prediction: A Decision-Aware Framework for Actionable Uncertainty Quantification](https://mlsanity.com/paper/2410.01767/) (2024)
- [Conformal Risk Training: End-to-End Optimization of Conformal Risk Control](https://mlsanity.com/paper/2510.08748/) (2025)
- [Conformal Policy Control](https://mlsanity.com/paper/2603.02196/) (2026)
- [Optimal Decision-Making Based on Prediction Sets](https://mlsanity.com/paper/2602.00989/) (2026)
- [Fast and Reliable N-k Contingency Screening with Input-Convex Neural Networks](https://mlsanity.com/paper/2410.00796/) (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)
- [Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees](https://mlsanity.com/paper/2506.03531/) (2025)
- [Risk-Controlled Post-Processing of Decision Policies](https://mlsanity.com/paper/2605.06479/) (2026)
- [Learning Polyhedral Conformal Sets for Robust Optimization](https://mlsanity.com/paper/2605.08506/) (2026)
- [Conformal Risk Sharing: Certified Cost Allocation with Participation Guarantees](https://mlsanity.com/paper/2606.06391/) (2026)
- [Threshold-Aware Conformal Routing](https://mlsanity.com/paper/2610.02487/) (2026)

## Abstract (arXiv)

Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to achieve with neural networks. Moreover, in high-dimensional settings, there may be many valid uncertainty estimates, each with its own performance profile - i.e., not all uncertainty is equally valuable for downstream decision-making. To address this problem, this paper develops an end-to-end framework to learn uncertainty sets for conditional robust optimization in a way that is informed by the downstream decision-making loss, with robustness and calibration guarantees provided by conformal prediction. In addition, we propose to represent general convex uncertainty sets with partially input-convex neural networks, which are learned as part of our framework. Our approach consistently improves upon two-stage estimate-then-optimize baselines on concrete applications in energy storage arbitrage and portfolio optimization.