# Conformal Risk Training: End-to-End Optimization of Conformal Risk Control

arXiv: https://arxiv.org/abs/2510.08748 · HTML: https://mlsanity.com/paper/2510.08748/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 54 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Builds on (most cited first, 30 of 31)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Kvasir-SEG: A Segmented Polyp Dataset](https://mlsanity.com/paper/1911.07069/) (2019)
- [Res2Net: A New Multi-scale Backbone Architecture](https://mlsanity.com/paper/1904.01169/) (2019)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [PraNet: Parallel Reverse Attention Network for Polyp Segmentation](https://mlsanity.com/paper/2006.11392/) (2020)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [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)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Differentiating Through a Cone Program](https://mlsanity.com/paper/1904.09043/) (2019)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control](https://mlsanity.com/paper/2302.03791/) (2023)
- [Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions](https://mlsanity.com/paper/2310.05921/) (2023)
- [Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents](https://mlsanity.com/paper/2502.02561/) (2025)
- [Learning Bounds for Risk-sensitive Learning](https://mlsanity.com/paper/2006.08138/) (2020)
- [On the Differentiability of the Solution to Convex Optimization Problems](https://mlsanity.com/paper/1804.05098/) (2018)
- [An Information Theoretic Perspective on Conformal Prediction](https://mlsanity.com/paper/2405.02140/) (2024)
- [Conformal Linguistic Calibration: Trading-off between Factuality and Specificity](https://mlsanity.com/paper/2502.19110/) (2025)
- [Regret Bounds for Markov Decision Processes with Recursive Optimized Certainty Equivalents](https://mlsanity.com/paper/2301.12601/) (2023)
- [End-to-End Conformal Calibration for Optimization Under Uncertainty](https://mlsanity.com/paper/2409.20534/) (2024)
- [Utility-Directed Conformal Prediction: A Decision-Aware Framework for Actionable Uncertainty Quantification](https://mlsanity.com/paper/2410.01767/) (2024)
- [Conformal Tail Risk Control for Large Language Model Alignment](https://mlsanity.com/paper/2502.20285/) (2025)
- [Supervised Learning with General Risk Functionals](https://mlsanity.com/paper/2206.13648/) (2022)

## Built on by (most cited first, 11 of 11)

- [CORA: Conformal Risk-Controlled Agents for Safeguarded Mobile GUI Automation](https://mlsanity.com/paper/2604.09155/) (2026)
- [Conformal Policy Control](https://mlsanity.com/paper/2603.02196/) (2026)
- [Optimized Certainty Equivalent Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2602.13660/) (2026)
- [Adversarially Robust Control of Conditional Value-at-Risk via Rockafellar-Uryasev Conformal Inference](https://mlsanity.com/paper/2606.00320/) (2026)
- [Decision-calibrated prediction sets for robust power system operations](https://mlsanity.com/paper/2606.02081/) (2026)
- [Decision-Focused Learning: When and Why Traditional Prediction Models Fail](https://mlsanity.com/paper/2606.21773/) (2026)
- [Conformal Risk Sharing: Certified Cost Allocation with Participation Guarantees](https://mlsanity.com/paper/2606.06391/) (2026)
- [SPACR: Single-Pass Adaptive Training of Uncertainty-Aware Conformal Regressors](https://mlsanity.com/paper/2606.10734/) (2026)
- [TRUST: Threshold-Recalibrated Uncertainty-Safe Training for Certified Dismissal in Breast Cancer Screening](https://mlsanity.com/paper/2609.00300/) (2026)
- [Occupancy-based Quantile Risk Control](https://mlsanity.com/paper/2609.03104/) (2026)
- [Tail-Aware Geometry Learning for Conformal Ellipsoids](https://mlsanity.com/paper/2609.27221/) (2026)

## Abstract (arXiv)

While deep learning models often achieve high predictive accuracy, their predictions typically do not come with any provable guarantees on risk or reliability, which are critical for deployment in high-stakes applications. The framework of conformal risk control (CRC) provides a distribution-free, finite-sample method for controlling the expected value of any bounded monotone loss function and can be conveniently applied post-hoc to any pre-trained deep learning model. However, many real-world applications are sensitive to tail risks, as opposed to just expected loss. In this work, we develop a method for controlling the general class of Optimized Certainty-Equivalent (OCE) risks, a broad class of risk measures which includes as special cases the expected loss (generalizing the original CRC method) and common tail risks like the conditional value-at-risk (CVaR). Furthermore, standard post-hoc CRC can degrade average-case performance due to its lack of feedback to the model. To address this, we introduce "conformal risk training," an end-to-end approach that differentiates through conformal OCE risk control during model training or fine-tuning. Our method achieves provable risk guarantees while demonstrating significantly improved average-case performance over post-hoc approaches on applications to controlling classifiers' false negative rate and controlling financial risk in battery storage operation.