# Conformal Contextual Robust Optimization

arXiv: https://arxiv.org/abs/2310.10003 · HTML: https://mlsanity.com/paper/2310.10003/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 73 references that are in the map.
- First posted on arXiv 16 Oct 2023.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Deep Learning for Precipitation Nowcasting: A Benchmark and A New Model](https://mlsanity.com/paper/1706.03458/) (2017)
- [Benchmarking Simulation-Based Inference](https://mlsanity.com/paper/2101.04653/) (2021)
- [OSMnx: New Methods for Acquiring, Constructing, Analyzing, and Visualizing Complex Street Networks](https://mlsanity.com/paper/1611.01890/) (2016)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Machine Learning for Precipitation Nowcasting from Radar Images](https://mlsanity.com/paper/1912.12132/) (2019)
- [Latent diffusion models for generative precipitation nowcasting with accurate uncertainty quantification](https://mlsanity.com/paper/2304.12891/) (2023)
- [Conformal Prediction Under Feedback Covariate Shift for Biomolecular Design](https://mlsanity.com/paper/2202.03613/) (2022)
- [Decision Trees for Decision-Making under the Predict-then-Optimize Framework](https://mlsanity.com/paper/2003.00360/) (2020)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [Probabilistic Conformal Prediction Using Conditional Random Samples](https://mlsanity.com/paper/2206.06584/) (2022)
- [GFlowNet-EM for learning compositional latent variable models](https://mlsanity.com/paper/2302.06576/) (2023)
- [Conffusion: Confidence Intervals for Diffusion Models](https://mlsanity.com/paper/2211.09795/) (2022)
- [Principal Uncertainty Quantification with Spatial Correlation for Image Restoration Problems](https://mlsanity.com/paper/2305.10124/) (2023)
- [Valid model-free spatial prediction](https://mlsanity.com/paper/2006.15640/) (2020)
- [Predict-then-Calibrate: A New Perspective of Robust Contextual LP](https://mlsanity.com/paper/2305.15686/) (2023)
- [Forward Amortized Inference for Likelihood-Free Variational Marginalization](https://mlsanity.com/paper/1805.11542/) (2018)
- [Physics Constrained Motion Prediction with Uncertainty Quantification](https://mlsanity.com/paper/2302.01060/) (2023)

## Built on by (most cited first, 25 of 25)

- [Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents](https://mlsanity.com/paper/2502.02561/) (2025)
- [Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making](https://mlsanity.com/paper/2502.05468/) (2025)
- [End-to-end Conditional Robust Optimization](https://mlsanity.com/paper/2403.04670/) (2024)
- [End-to-End Conformal Calibration for Optimization Under Uncertainty](https://mlsanity.com/paper/2409.20534/) (2024)
- [Utility-Directed Conformal Prediction: A Decision-Aware Framework for Actionable Uncertainty Quantification](https://mlsanity.com/paper/2410.01767/) (2024)
- [Conformal Prediction for Ensembles: Improving Efficiency via Score-Based Aggregation](https://mlsanity.com/paper/2405.16246/) (2024)
- [Conformalized Interval Arithmetic with Symmetric Calibration](https://mlsanity.com/paper/2408.10939/) (2024)
- [Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regression](https://mlsanity.com/paper/2503.02205/) (2025)
- [Enhanced Route Planning with Calibrated Uncertainty Set](https://mlsanity.com/paper/2503.10088/) (2025)
- [Calibrating Decision Robustness via Inverse Conformal Risk Control](https://mlsanity.com/paper/2510.07750/) (2025)
- [Optimal Decision-Making Based on Prediction Sets](https://mlsanity.com/paper/2602.00989/) (2026)
- [A Conformal Approach to Feature-based Newsvendor under Model Misspecification](https://mlsanity.com/paper/2412.13159/) (2024)
- [Enhancing Electricity-System Resilience with Adaptive Robust Optimization and Conformal Uncertainty Characterization](https://mlsanity.com/paper/2505.11627/) (2025)
- [Conformalized Decision Risk Assessment](https://mlsanity.com/paper/2505.13243/) (2025)
- [Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints](https://mlsanity.com/paper/2505.22881/) (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)
- [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)
- [Conformal-DRO: Distributionally Robust Optimization with Conformalized Ambiguity Set](https://mlsanity.com/paper/2609.11073/) (2026)
- [Adaptive Conformal Prediction for Quantum Machine Learning](https://mlsanity.com/paper/2511.18225/) (2025)
- [Distribution-Free Robust Predict-Then-Optimize in Function Spaces](https://mlsanity.com/paper/2602.08215/) (2026)
- [Contextual Preference Distribution Learning](https://mlsanity.com/paper/2603.17139/) (2026)
- [Smart predict-then-robustly-optimize](https://mlsanity.com/paper/2607.21773/) (2026)
- [Counterfactual Online Conformal Prediction Under Adaptive Logging](https://mlsanity.com/paper/2609.30811/) (2026)

## Abstract (arXiv)

Data-driven approaches to predict-then-optimize decision-making problems seek to mitigate the risk of uncertainty region misspecification in safety-critical settings. Current approaches, however, suffer from considering overly conservative uncertainty regions, often resulting in suboptimal decisionmaking. To this end, we propose Conformal-Predict-Then-Optimize (CPO), a framework for leveraging highly informative, nonconvex conformal prediction regions over high-dimensional spaces based on conditional generative models, which have the desired distribution-free coverage guarantees. Despite guaranteeing robustness, such black-box optimization procedures alone inspire little confidence owing to the lack of explanation of why a particular decision was found to be optimal. We, therefore, augment CPO to additionally provide semantically meaningful visual summaries of the uncertainty regions to give qualitative intuition for the optimal decision. We highlight the CPO framework by demonstrating results on a suite of simulation-based inference benchmark tasks and a vehicle routing task based on probabilistic weather prediction.