# Tightening optimality gap with confidence through conformal prediction

arXiv: https://arxiv.org/abs/2503.04071 · HTML: https://mlsanity.com/paper/2503.04071/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 45 references that are in the map.
- First posted on arXiv 6 Mar 2025.

## Builds on (most cited first, 20 of 20)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Parallelizing the dual revised simplex method](https://mlsanity.com/paper/1503.01889/) (2015)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms](https://mlsanity.com/paper/1908.02788/) (2019)
- [Selection and Aggregation of Conformal Prediction Sets](https://mlsanity.com/paper/2104.13871/) (2021)
- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [RAYEN: Imposition of Hard Convex Constraints on Neural Networks](https://mlsanity.com/paper/2307.08336/) (2023)
- [A Convex Neural Network Solver for DCOPF with Generalization Guarantees](https://mlsanity.com/paper/2009.09109/) (2020)
- [Dual Conic Proxies for AC Optimal Power Flow](https://mlsanity.com/paper/2310.02969/) (2023)
- [Dual Lagrangian Learning for Conic Optimization](https://mlsanity.com/paper/2402.03086/) (2024)
- [Conformal Frequency Estimation using Discrete Sketched Data with Coverage for Distinct Queries](https://mlsanity.com/paper/2211.04612/) (2022)
- [Learning Optimal Power Flow Value Functions with Input-Convex Neural Networks](https://mlsanity.com/paper/2310.04605/) (2023)
- [Real-Time Risk Analysis with Optimization Proxies](https://mlsanity.com/paper/2310.00709/) (2023)
- [Dual Interior Point Optimization Learning](https://mlsanity.com/paper/2402.02596/) (2024)
- [Learning optimal objective values for MILP](https://mlsanity.com/paper/2411.18321/) (2024)

## Built on by (most cited first, 2 of 2)

- [Conformal Predictive Distributions for Order Fulfillment Time Forecasting](https://mlsanity.com/paper/2505.17340/) (2025)
- [Differentially Private Conformal Prediction via Quantile Binary Search](https://mlsanity.com/paper/2507.12497/) (2025)

## Abstract (arXiv)

Decision makers routinely use constrained optimization technology to plan and operate complex systems like global supply chains or power grids. In this context, practitioners must assess how close a computed solution is to optimality in order to make operational decisions, such as whether the current solution is sufficient or whether additional computation is warranted. A common practice is to evaluate solution quality using dual bounds returned by optimization solvers. While these dual bounds come with certified guarantees, they are often too loose to be practically informative. To this end, this paper introduces a novel conformal prediction framework for tightening loose primal and dual bounds. The proposed method addresses the heteroskedasticity commonly observed in these bounds via selective inference, and further exploits their inherent certified validity to produce tighter, more informative prediction intervals. Finally, numerical experiments on large-scale industrial problems suggest that the proposed approach can provide the same coverage level more efficiently than baseline methods.