# Learning Joint Models of Prediction and Optimization

arXiv: https://arxiv.org/abs/2409.04898 · HTML: https://mlsanity.com/paper/2409.04898/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 32 references that are in the map.
- First posted on arXiv 7 Sep 2024.

## Builds on (most cited first, 25 of 25)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [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)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Learning Scheduling Algorithms for Data Processing Clusters](https://mlsanity.com/paper/1810.01963/) (2018)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [Interior Point Solving for LP-based prediction+optimisation](https://mlsanity.com/paper/2010.13943/) (2020)
- [Lagrangian Duality for Constrained Deep Learning](https://mlsanity.com/paper/2001.09394/) (2020)
- [Differentiating Through a Cone Program](https://mlsanity.com/paper/1904.09043/) (2019)
- [Learning Combinatorial Optimization on Graphs: A Survey with Applications to Networking](https://mlsanity.com/paper/2005.11081/) (2020)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [End-to-End Learning to Warm-Start for Real-Time Quadratic Optimization](https://mlsanity.com/paper/2212.08260/) (2022)
- [Leaving the Nest: Going Beyond Local Loss Functions for Predict-Then-Optimize](https://mlsanity.com/paper/2305.16830/) (2023)
- [Landscape Surrogate: Learning Decision Losses for Mathematical Optimization Under Partial Information](https://mlsanity.com/paper/2307.08964/) (2023)
- [Backpropagation of Unrolled Solvers with Folded Optimization](https://mlsanity.com/paper/2301.12047/) (2023)
- [NESTA, The NICTA Energy System Test Case Archive](https://mlsanity.com/paper/1411.0359/) (2014)

## Built on by (most cited first, 3 of 3)

- [Sufficient Decision Proxies for Decision-Focused Learning](https://mlsanity.com/paper/2505.03953/) (2025)
- [Imitation Learning for Combinatorial Optimisation under Uncertainty](https://mlsanity.com/paper/2601.05383/) (2026)
- [Scalable Decision-Focused Learning through Cost-Sensitive Regression](https://mlsanity.com/paper/2605.18005/) (2026)

## Abstract (arXiv)

The Predict-Then-Optimize framework uses machine learning models to predict unknown parameters of an optimization problem from exogenous features before solving. This setting is common to many real-world decision processes, and recently it has been shown that decision quality can be substantially improved by solving and differentiating the optimization problem within an end-to-end training loop. However, this approach requires significant computational effort in addition to handcrafted, problem-specific rules for backpropagation through the optimization step, challenging its applicability to a broad class of optimization problems. This paper proposes an alternative method, in which optimal solutions are learned directly from the observable features by joint predictive models. The approach is generic, and based on an adaptation of the Learning-to-Optimize paradigm, from which a rich variety of existing techniques can be employed. Experimental evaluations show the ability of several Learning-to-Optimize methods to provide efficient and accurate solutions to an array of challenging Predict-Then-Optimize problems.