# Bridging conformal prediction and scenario optimization

arXiv: https://arxiv.org/abs/2503.23561 · HTML: https://mlsanity.com/paper/2503.23561/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 30 Mar 2025.

## Builds on (most cited first, 9 of 9)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Formal Verification and Control with Conformal Prediction](https://mlsanity.com/paper/2409.00536/) (2024)
- [Verification of Neural Reachable Tubes via Scenario Optimization and Conformal Prediction](https://mlsanity.com/paper/2312.08604/) (2023)
- [Compression, Generalization and Learning](https://mlsanity.com/paper/2301.12767/) (2023)
- [Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractions](https://mlsanity.com/paper/2301.01526/) (2023)
- [On the exact feasibility of convex scenario programs with discarded constraints](https://mlsanity.com/paper/2003.13433/) (2020)
- [A Theory of the Risk for Optimization with Relaxation and its Application to Support Vector Machines](https://mlsanity.com/paper/2004.05839/) (2020)
- [Conformal Off-Policy Evaluation in Markov Decision Processes](https://mlsanity.com/paper/2304.02574/) (2023)
- [Prediction error quantification through probabilistic scaling -- EXTENDED VERSION](https://mlsanity.com/paper/2105.14187/) (2021)

## Built on by (most cited first, 5 of 5)

- [Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Tasks](https://mlsanity.com/paper/2508.11025/) (2025)
- [Bridging Conformal Prediction and Scenario Optimization: Discarded Constraints and Modular Risk Allocation](https://mlsanity.com/paper/2603.19396/) (2026)
- [Multi-Variable Conformal Prediction: Optimizing Prediction Sets without Data Splitting](https://mlsanity.com/paper/2605.12341/) (2026)
- [A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification](https://mlsanity.com/paper/2608.29789/) (2026)
- [Exact Risk-Complexity Laws for Projective Boundaries in Scenario Optimization and Distribution-Free Certification](https://mlsanity.com/paper/2609.01355/) (2026)

## Abstract (arXiv)

Conformal prediction and scenario optimization constitute two important classes of statistical learning frameworks to certify decisions made using data. They have found numerous applications in control theory, machine learning and robotics. Despite intense research in both areas, and apparently similar results, a clear connection between these two frameworks has not been established. By focusing on the so-called vanilla conformal prediction, we show rigorously how to choose appropriate score functions and set predictor map to recover well-known bounds on the probability of constraint violation associated with scenario programs. We also show how to treat ranking of nonconformity scores as a one-dimensional scenario program with discarded constraints, and use such connection to recover vanilla conformal prediction guarantees on the validity of the set predictor. We also capitalize on the main developments of the scenario approach, and show how we could analyze calibration conditional conformal prediction under this lens. Our results establish a theoretical bridge between conformal prediction and scenario optimization.