# End-to-End Learning for Fair Multiobjective Optimization Under Uncertainty

arXiv: https://arxiv.org/abs/2402.07772 · HTML: https://mlsanity.com/paper/2402.07772/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 12 Feb 2024.

## Builds on (most cited first, 17 of 17)

- [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)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [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)
- [Fast Differentiable Sorting and Ranking](https://mlsanity.com/paper/2002.08871/) (2020)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Interior Point Solving for LP-based prediction+optimisation](https://mlsanity.com/paper/2010.13943/) (2020)
- [Differentiating Through a Cone Program](https://mlsanity.com/paper/1904.09043/) (2019)
- [Gradient Estimation with Stochastic Softmax Tricks](https://mlsanity.com/paper/2006.08063/) (2020)
- [The Complexity of Large-scale Convex Programming under a Linear Optimization Oracle](https://mlsanity.com/paper/1309.5550/) (2013)
- [Two-sided fairness in rankings via Lorenz dominance](https://mlsanity.com/paper/2110.15781/) (2021)
- [The Limited Multi-Label Projection Layer](https://mlsanity.com/paper/1906.08707/) (2019)
- [End-to-end Learning for Fair Ranking Systems](https://mlsanity.com/paper/2111.10723/) (2021)
- [Optimizing generalized Gini indices for fairness in rankings](https://mlsanity.com/paper/2204.06521/) (2022)
- [Backpropagation of Unrolled Solvers with Folded Optimization](https://mlsanity.com/paper/2301.12047/) (2023)
- [Multi-Task Predict-then-Optimize](https://mlsanity.com/paper/2212.05403/) (2022)

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

- [End-to-End Fairness Optimization with Fair Decision-Focused Learning](https://mlsanity.com/paper/2607.29441/) (2026)
- [Decision-Focused Continual Learning for Seaport Power-Logistics Scheduling: Generalization across Varying Tasks](https://mlsanity.com/paper/2511.07938/) (2025)

## Abstract (arXiv)

Many decision processes in artificial intelligence and operations research are modeled by parametric optimization problems whose defining parameters are unknown and must be inferred from observable data. The Predict-Then-Optimize (PtO) paradigm in machine learning aims to maximize downstream decision quality by training the parametric inference model end-to-end with the subsequent constrained optimization. This requires backpropagation through the optimization problem using approximation techniques specific to the problem's form, especially for nondifferentiable linear and mixed-integer programs. This paper extends the PtO methodology to optimization problems with nondifferentiable Ordered Weighted Averaging (OWA) objectives, known for their ability to ensure properties of fairness and robustness in decision models. Through a collection of training techniques and proposed application settings, it shows how optimization of OWA functions can be effectively integrated with parametric prediction for fair and robust optimization under uncertainty.