# Conformal Risk Control for Non-Monotonic Losses

arXiv: https://arxiv.org/abs/2602.20151 · HTML: https://mlsanity.com/paper/2602.20151/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 49 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [PraNet: Parallel Reverse Attention Network for Polyp Segmentation](https://mlsanity.com/paper/2006.11392/) (2020)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Multiaccuracy: Black-Box Post-Processing for Fairness in Classification](https://mlsanity.com/paper/1805.12317/) (2018)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Learning by Transduction](https://mlsanity.com/paper/1301.7375/) (2013)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [Sharper bounds for uniformly stable algorithms](https://mlsanity.com/paper/1910.07833/) (2019)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [Practical Adversarial Multivalid Conformal Prediction](https://mlsanity.com/paper/2206.01067/) (2022)
- [Generalization Bounds for Uniformly Stable Algorithms](https://mlsanity.com/paper/1812.09859/) (2018)
- [How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control](https://mlsanity.com/paper/2302.03791/) (2023)
- [Conformal Validity Guarantees Exist for Any Data Distribution (and How to Find Them)](https://mlsanity.com/paper/2405.06627/) (2024)
- [Efficiently Controlling Multiple Risks with Pareto Testing](https://mlsanity.com/paper/2210.07913/) (2022)
- [Automatically Adaptive Conformal Risk Control](https://mlsanity.com/paper/2406.17819/) (2024)
- [Black-box tests for algorithmic stability](https://mlsanity.com/paper/2111.15546/) (2021)
- [Gradient Equilibrium in Online Learning: Theory and Applications](https://mlsanity.com/paper/2501.08330/) (2025)
- [Post-Selection Inference via Algorithmic Stability](https://mlsanity.com/paper/2011.09462/) (2020)

## Built on by (most cited first, 8 of 8)

- [Conformal Policy Control](https://mlsanity.com/paper/2603.02196/) (2026)
- [A Joint Finite-Sample Certificate for Adaptive Selective Conformal Risk Control](https://mlsanity.com/paper/2606.08517/) (2026)
- [Conformal Risk Control under Non-Monotone Losses: Theory and Finite-Sample Guarantees](https://mlsanity.com/paper/2604.01502/) (2026)
- [Risk-Controlled Post-Processing of Decision Policies](https://mlsanity.com/paper/2605.06479/) (2026)
- [Certified Domain Consistency for Multi-Domain Retrieval: Label-Free Per-Domain Contamination Control with Conformal Risk Guarantees](https://mlsanity.com/paper/2607.14157/) (2026)
- [ReCIRC: Rectified Conformal Risk Control](https://mlsanity.com/paper/2609.38112/) (2026)
- [Valid Stopping in Adaptive Generator-Verifier Loops](https://mlsanity.com/paper/2610.06432/) (2026)
- [CARE: Certifying Acceleration for Vision-Language-Action Inference](https://mlsanity.com/paper/2610.08917/) (2026)

## Abstract (arXiv)

Conformal risk control is an extension of conformal prediction for controlling risk functions beyond miscoverage. The original algorithm controls the expected value of a loss that is monotonic in a one-dimensional parameter. Here, we present risk control guarantees for generic algorithms applied to possibly non-monotonic losses with multidimensional parameters. The guarantees depend on the stability of the algorithm -- unstable algorithms have looser guarantees. We give applications of this technique to selective image classification, FDR and IOU control of tumor segmentations, and multigroup debiasing of recidivism predictions across overlapping race and sex groups using empirical risk minimization.