# Bridging Conformal Prediction and Scenario Optimization: Discarded Constraints and Modular Risk Allocation

arXiv: https://arxiv.org/abs/2603.19396 · HTML: https://mlsanity.com/paper/2603.19396/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 26 references that are in the map.
- First posted on arXiv 19 Mar 2026.

## Builds on (most cited first, 8 of 8)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Adaptive Conformal Prediction for Motion Planning among Dynamic Agents](https://mlsanity.com/paper/2212.00278/) (2022)
- [Stable Sample Compression Schemes: New Applications and an Optimal SVM Margin Bound](https://mlsanity.com/paper/2011.04586/) (2020)
- [The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violations](https://mlsanity.com/paper/1307.5640/) (2013)
- [Compression, Generalization and Learning](https://mlsanity.com/paper/2301.12767/) (2023)
- [On the exact feasibility of convex scenario programs with discarded constraints](https://mlsanity.com/paper/2003.13433/) (2020)
- [Signal Temporal Logic Control Synthesis among Uncontrollable Dynamic Agents with Conformal Prediction](https://mlsanity.com/paper/2312.04242/) (2023)
- [Bridging conformal prediction and scenario optimization](https://mlsanity.com/paper/2503.23561/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification](https://mlsanity.com/paper/2608.29789/) (2026)

## Abstract (arXiv)

Scenario optimization and conformal prediction share a common goal, that is, turning finite samples into safety margins. Yet, different terminology often obscures the connection between their respective guarantees. This paper revisits that connection directly from a systems-and-control viewpoint. Building on the recent conformal/scenario bridge of citetOSullivanRomaoMargellos2026, we extend the forward direction to feasible sample-and-discard scenario algorithms. Specifically, if the final decision is determined by a stable subset of the retained sampled constraints, the classical mean violation law admits a direct exchangeability-based derivation. In this view, discarded samples naturally appear as admissible exceptions. We also introduce a simple modular composition rule that combines several blockwise calibration certificates into a single joint guarantee. This rule proves particularly useful in multi-output prediction and finite-horizon control, where engineers must distribute risk across coordinates, constraints, or prediction steps. Finally, we provide numerical illustrations using a calibrated multi-step tube around an identified predictor. These examples compare alternative stage-wise risk allocations and highlight the resulting performance and safety trade-offs in a standard constraint-tightening problem.