# Two-Stage Predict+Optimize for Mixed Integer Linear Programs with Unknown Parameters in Constraints

arXiv: https://arxiv.org/abs/2311.08022 · HTML: https://mlsanity.com/paper/2311.08022/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 27 references that are in the map.
- First posted on arXiv 14 Nov 2023.

## Builds on (most cited first, 14 of 14)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [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-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [Decision Trees for Decision-Making under the Predict-then-Optimize Framework](https://mlsanity.com/paper/2003.00360/) (2020)
- [Contrastive Losses and Solution Caching for Predict-and-Optimize](https://mlsanity.com/paper/2011.05354/) (2020)
- [CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints](https://mlsanity.com/paper/2105.02343/) (2021)
- [Enforcing Policy Feasibility Constraints through Differentiable Projection for Energy Optimization](https://mlsanity.com/paper/2105.08881/) (2021)
- [Predict+Optimize for Packing and Covering LPs with Unknown Parameters in Constraints](https://mlsanity.com/paper/2209.03668/) (2022)
- [Branch & Learn for Recursively and Iteratively Solvable Problems in Predict+Optimize](https://mlsanity.com/paper/2205.01672/) (2022)
- [A Solver-Free Framework for Scalable Learning in Neural ILP Architectures](https://mlsanity.com/paper/2210.09082/) (2022)

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

- [Sufficient Decision Proxies for Decision-Focused Learning](https://mlsanity.com/paper/2505.03953/) (2025)

## Abstract (arXiv)

Consider the setting of constrained optimization, with some parameters unknown at solving time and requiring prediction from relevant features. Predict+Optimize is a recent framework for end-to-end training supervised learning models for such predictions, incorporating information about the optimization problem in the training process in order to yield better predictions in terms of the quality of the predicted solution under the true parameters. Almost all prior works have focused on the special case where the unknowns appear only in the optimization objective and not the constraints. Hu et al.~proposed the first adaptation of Predict+Optimize to handle unknowns appearing in constraints, but the framework has somewhat ad-hoc elements, and they provided a training algorithm only for covering and packing linear programs. In this work, we give a new simpler and more powerful framework called Two-Stage Predict+Optimize, which we believe should be the canonical framework for the Predict+Optimize setting. We also give a training algorithm usable for all mixed integer linear programs, vastly generalizing the applicability of the framework. Experimental results demonstrate the superior prediction performance of our training framework over all classical and state-of-the-art methods.