# Conformal Predictive Programming for Chance Constrained Optimization

arXiv: https://arxiv.org/abs/2402.07407 · HTML: https://mlsanity.com/paper/2402.07407/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 97 references that are in the map.
- First posted on arXiv 12 Feb 2024.

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

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [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)
- [Class-Conditional Conformal Prediction with Many Classes](https://mlsanity.com/paper/2306.09335/) (2023)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [Prediction and outlier detection in classification problems](https://mlsanity.com/paper/1905.04396/) (2019)
- [Exchangeability, Conformal Prediction, and Rank Tests](https://mlsanity.com/paper/2005.06095/) (2020)
- [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023)
- [Verification of Neural Reachable Tubes via Scenario Optimization and Conformal Prediction](https://mlsanity.com/paper/2312.08604/) (2023)
- [Safe Reinforcement Learning with Chance-constrained Model Predictive Control](https://mlsanity.com/paper/2112.13941/) (2021)
- [On Distributionally Robust Chance Constrained Programs with Wasserstein Distance](https://mlsanity.com/paper/1806.07418/) (2018)
- [Robust Conformal Prediction for STL Runtime Verification under Distribution Shift](https://mlsanity.com/paper/2311.09482/) (2023)
- [Data-Driven Chance Constrained Programs over Wasserstein Balls](https://mlsanity.com/paper/1809.00210/) (2018)
- [Solving Chance-Constrained Problems via a Smooth Sample-Based Nonlinear Approximation](https://mlsanity.com/paper/1905.07377/) (2019)
- [A scenario approach for non-convex control design](https://mlsanity.com/paper/1401.2200/) (2014)
- [High-Confidence Data-Driven Ambiguity Sets for Time-Varying Linear Systems](https://mlsanity.com/paper/2102.01142/) (2021)
- [Trajectory Optimization of Chance-Constrained Nonlinear Stochastic Systems for Motion Planning Under Uncertainty](https://mlsanity.com/paper/2106.02801/) (2021)
- [Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets](https://mlsanity.com/paper/1805.06729/) (2018)
- [A Posteriori Probabilistic Bounds of Convex Scenario Programs with Validation Tests](https://mlsanity.com/paper/1903.11734/) (2019)
- [Chance-Constrained Trajectory Optimization for Non-linear Systems with Unknown Stochastic Dynamics](https://mlsanity.com/paper/1906.11003/) (2019)
- [An Empirical Quantile Estimation Approach to Nonlinear Optimization Problems with Chance Constraints](https://mlsanity.com/paper/2211.00675/) (2022)
- [Chance-Constrained Trajectory Optimization for High-DOF Robots in Uncertain Environments](https://mlsanity.com/paper/2302.00122/) (2023)

## Built on by (most cited first, 6 of 6)

- [Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents](https://mlsanity.com/paper/2502.02561/) (2025)
- [Conformal Risk-Averse Decision Making with Action Conditional Guarantee](https://mlsanity.com/paper/2606.05551/) (2026)
- [Conformal Mixed-Integer Constraint Learning with Feasibility Guarantees](https://mlsanity.com/paper/2506.03531/) (2025)
- [Learning Polyhedral Conformal Sets for Robust Optimization](https://mlsanity.com/paper/2605.08506/) (2026)
- [Statistical Contraction for Chance-Constrained Trajectory Optimization of Non-Gaussian Stochastic Systems](https://mlsanity.com/paper/2603.07092/) (2026)
- [A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification](https://mlsanity.com/paper/2608.29789/) (2026)

## Abstract (arXiv)

We propose conformal predictive programming (CPP), a framework to solve chance constrained optimization problems, i.e., optimization problems with constraints that are functions of random variables. CPP utilizes samples from these random variables along with the quantile lemma - central to conformal prediction - to transform the chance constrained optimization problem into a deterministic problem with a quantile reformulation. CPP's main strength is an independent calibration step that provides a posteriori guarantees for the solution of this problem that are of conditional and marginal nature otherwise. These guarantees even apply in settings when assumptions required for obtaining standard a priori guarantees (e.g., in scenario optimization or sample average approximation) are unavailable, difficult to compute, or conservative. Another strength of CPP is that it can easily support different variants of conformal prediction which have been (or will be) proposed within the conformal prediction community. To illustrate this, we present robust CPP to deal with distribution shifts in the random variables and Mondrian CPP to deal with class conditional chance constraints. In a series of case studies, we show the validity of the aforementioned approaches, and illustrate the advantage of CPP as compared to scenario approach.