# Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents

arXiv: https://arxiv.org/abs/2502.02561 · HTML: https://mlsanity.com/paper/2502.02561/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 80 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 30 of 43)

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Can AI help in screening Viral and COVID-19 pneumonia?](https://mlsanity.com/paper/2003.13145/) (2020)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibration](https://mlsanity.com/paper/2107.05719/) (2021)
- [Batch Multivalid Conformal Prediction](https://mlsanity.com/paper/2209.15145/) (2022)
- [Practical Adversarial Multivalid Conformal Prediction](https://mlsanity.com/paper/2206.01067/) (2022)
- [Moment Multicalibration for Uncertainty Estimation](https://mlsanity.com/paper/2008.08037/) (2020)
- [Improving Expert Predictions with Conformal Prediction](https://mlsanity.com/paper/2201.12006/) (2022)
- [Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions](https://mlsanity.com/paper/2310.05921/) (2023)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [Inverse Optimization: Theory and Applications](https://mlsanity.com/paper/2109.03920/) (2021)
- [PAC Prediction Sets Under Covariate Shift](https://mlsanity.com/paper/2106.09848/) (2021)
- [High-Dimensional Prediction for Sequential Decision Making](https://mlsanity.com/paper/2310.17651/) (2023)
- [Length Optimization in Conformal Prediction](https://mlsanity.com/paper/2406.18814/) (2024)
- [Formal Verification and Control with Conformal Prediction](https://mlsanity.com/paper/2409.00536/) (2024)
- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [Forecasting for Swap Regret for All Downstream Agents](https://mlsanity.com/paper/2402.08753/) (2024)
- [Conformal Prediction with Learned Features](https://mlsanity.com/paper/2404.17487/) (2024)
- [Computationally efficient versions of conformal predictive distributions](https://mlsanity.com/paper/1911.00941/) (2019)
- [End-to-end Conditional Robust Optimization](https://mlsanity.com/paper/2403.04670/) (2024)

## Built on by (most cited first, 30 of 40)

- [Conformal Calibration: Ensuring the Reliability of Black-Box AI in Wireless Systems](https://mlsanity.com/paper/2504.09310/) (2025)
- [Conformal Risk Training: End-to-End Optimization of Conformal Risk Control](https://mlsanity.com/paper/2510.08748/) (2025)
- [Conformal Prediction and Human Decision Making](https://mlsanity.com/paper/2503.11709/) (2025)
- [Human-AI Collaborative Uncertainty Quantification](https://mlsanity.com/paper/2510.23476/) (2025)
- [Conformal Prediction Beyond the Seen: A Missing Mass Perspective for Uncertainty Quantification in Generative Models](https://mlsanity.com/paper/2506.05497/) (2025)
- [Conformal Policy Control](https://mlsanity.com/paper/2603.02196/) (2026)
- [Multi-Condition Conformal Selection](https://mlsanity.com/paper/2510.08075/) (2025)
- [Optimal Decision-Making Based on Prediction Sets](https://mlsanity.com/paper/2602.00989/) (2026)
- [Conformalized Decision Risk Assessment](https://mlsanity.com/paper/2505.13243/) (2025)
- [Optimal Conformal Prediction under Epistemic Uncertainty](https://mlsanity.com/paper/2505.19033/) (2025)
- [Fuzzy Prediction Sets: Conformal Prediction with E-values](https://mlsanity.com/paper/2509.13130/) (2025)
- [Robust Decision Making with Partially Calibrated Forecasts](https://mlsanity.com/paper/2510.23471/) (2025)
- [Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distributions to Multivariate Settings](https://mlsanity.com/paper/2511.15146/) (2025)
- [Multi-Round Human-AI Collaboration with User-Specified Requirements](https://mlsanity.com/paper/2602.17646/) (2026)
- [Constrained Diffusion Models for Synthesizing Representative Power Flow Datasets](https://mlsanity.com/paper/2506.11281/) (2025)
- [Extending Prediction-Powered Inference through Conformal Prediction](https://mlsanity.com/paper/2510.16166/) (2025)
- [Uncertainty Quantification and Data Efficiency in AI: An Information-Theoretic Perspective](https://mlsanity.com/paper/2512.05267/) (2025)
- [Beyond Procedure: Substantive Fairness in Conformal Prediction](https://mlsanity.com/paper/2602.16794/) (2026)
- [Conformal Risk-Averse Decision Making with Action Conditional Guarantee](https://mlsanity.com/paper/2606.05551/) (2026)
- [Decision Making Needs Uncertainty Quantification [Lecture Notes]](https://mlsanity.com/paper/2607.14407/) (2026)
- [Adaptive Cumulative Mass Calibration with Conformal Prediction](https://mlsanity.com/paper/2505.15437/) (2025)
- [Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees](https://mlsanity.com/paper/2506.03531/) (2025)
- [Reliable Inference in Edge-Cloud Model Cascades via Conformal Alignment](https://mlsanity.com/paper/2510.17543/) (2025)
- [Evaluating AI Grading on Real-World Handwritten College Mathematics: A Large-Scale Study Toward a Benchmark](https://mlsanity.com/paper/2603.00895/) (2026)
- [Elements of Conformal Prediction](https://mlsanity.com/paper/2603.23923/) (2026)
- [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)
- [Uncertainty-Aware Generation and Decision-Making Under Ambiguity](https://mlsanity.com/paper/2606.30578/) (2026)
- [Conformal Changepoint Localization and Root Cause Analysis with Corrupted Observations](https://mlsanity.com/paper/2607.26481/) (2026)
- [Online Conformal Prediction Beyond Feedback](https://mlsanity.com/paper/2608.07139/) (2026)

## Abstract (arXiv)

A fundamental question in data-driven decision making is how to quantify the uncertainty of predictions in ways that can usefully inform downstream action. This interface between prediction uncertainty and decision-making is especially important in risk-sensitive domains, such as medicine. In this paper, we develop decision-theoretic foundations that connect uncertainty quantification using prediction sets with risk-averse decision-making. Specifically, we answer three fundamental questions: (1) What is the correct notion of uncertainty quantification for risk-averse decision makers? We prove that prediction sets are optimal for decision makers who wish to optimize their value at risk. (2) What is the optimal policy that a risk averse decision maker should use to map prediction sets to actions? We show that a simple max-min decision policy is optimal for risk-averse decision makers. Finally, (3) How can we derive prediction sets that are optimal for such decision makers? We provide an exact characterization in the population regime and a distribution free finite-sample construction. Answering these questions naturally leads to an algorithm, Risk-Averse Calibration (RAC), which follows a provably optimal design for deriving action policies from predictions. RAC is designed to be both practical-capable of leveraging the quality of predictions in a black-box manner to enhance downstream utility-and safe-adhering to a user-defined risk threshold and optimizing the corresponding risk quantile of the user's downstream utility. Finally, we experimentally demonstrate the significant advantages of RAC in applications such as medical diagnosis and recommendation systems. Specifically, we show that RAC achieves a substantially improved trade-off between safety and utility, offering higher utility compared to existing methods while maintaining the safety guarantee.