# Predict+Optimize for Packing and Covering LPs with Unknown Parameters in Constraints

arXiv: https://arxiv.org/abs/2209.03668 · HTML: https://mlsanity.com/paper/2209.03668/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 8 Sep 2022.

## Builds on (most cited first, 7 of 7)

- [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)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Interior Point Solving for LP-based prediction+optimisation](https://mlsanity.com/paper/2010.13943/) (2020)
- [Decision Trees for Decision-Making under the Predict-then-Optimize Framework](https://mlsanity.com/paper/2003.00360/) (2020)
- [CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints](https://mlsanity.com/paper/2105.02343/) (2021)

## Built on by (most cited first, 11 of 11)

- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning](https://mlsanity.com/paper/2307.05213/) (2023)
- [Feasibility-Aware Decision-Focused Learning for Predicting Parameters in the Constraints](https://mlsanity.com/paper/2510.04951/) (2025)
- [Branch & Learn with Post-hoc Correction for Predict+Optimize with Unknown Parameters in Constraints](https://mlsanity.com/paper/2303.06698/) (2023)
- [Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints](https://mlsanity.com/paper/2505.22881/) (2025)
- [Two-Stage Predict+Optimize for Mixed Integer Linear Programs with Unknown Parameters in Constraints](https://mlsanity.com/paper/2311.08022/) (2023)
- [DFF: Decision-Focused Fine-tuning for Smarter Predict-then-Optimize with Limited Data](https://mlsanity.com/paper/2501.01874/) (2025)
- [Learning From Scenarios for Stochastic Repairable Scheduling](https://mlsanity.com/paper/2312.03492/) (2023)
- [Scalable Decision Focused Learning via Online Trainable Surrogates](https://mlsanity.com/paper/2512.03861/) (2025)
- [Imitation Learning for Combinatorial Optimisation under Uncertainty](https://mlsanity.com/paper/2601.05383/) (2026)
- [PolyStepOR: Learning to Decide Without Optimal Decisions](https://mlsanity.com/paper/2609.32465/) (2026)

## Abstract (arXiv)

Predict+Optimize is a recently proposed framework which combines machine learning and constrained optimization, tackling optimization problems that contain parameters that are unknown at solving time. The goal is to predict the unknown parameters and use the estimates to solve for an estimated optimal solution to the optimization problem. However, all prior works have focused on the case where unknown parameters appear only in the optimization objective and not the constraints, for the simple reason that if the constraints were not known exactly, the estimated optimal solution might not even be feasible under the true parameters. The contributions of this paper are two-fold. First, we propose a novel and practically relevant framework for the Predict+Optimize setting, but with unknown parameters in both the objective and the constraints. We introduce the notion of a correction function, and an additional penalty term in the loss function, modelling practical scenarios where an estimated optimal solution can be modified into a feasible solution after the true parameters are revealed, but at an additional cost. Second, we propose a corresponding algorithmic approach for our framework, which handles all packing and covering linear programs. Our approach is inspired by the prior work of Mandi and Guns, though with crucial modifications and re-derivations for our very different setting. Experimentation demonstrates the superior empirical performance of our method over classical approaches.