# Fairness in Multi-Task Learning via Wasserstein Barycenters

arXiv: https://arxiv.org/abs/2306.10155 · HTML: https://mlsanity.com/paper/2306.10155/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 52 references that are in the map.
- First posted on arXiv 16 Jun 2023.

## Builds on (most cited first, 24 of 24)

- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Which Tasks Should Be Learned Together in Multi-task Learning?](https://mlsanity.com/paper/1905.07553/) (2019)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Empirical Risk Minimization under Fairness Constraints](https://mlsanity.com/paper/1802.08626/) (2018)
- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [Gradient Vaccine: Investigating and Improving Multi-task Optimization in Massively Multilingual Models](https://mlsanity.com/paper/2010.05874/) (2020)
- [Fair Regression: Quantitative Definitions and Reduction-based Algorithms](https://mlsanity.com/paper/1905.12843/) (2019)
- [Wasserstein Fair Classification](https://mlsanity.com/paper/1907.12059/) (2019)
- [Fair Regression with Wasserstein Barycenters](https://mlsanity.com/paper/2006.07286/) (2020)
- [Leveraging Labeled and Unlabeled Data for Consistent Fair Binary Classification](https://mlsanity.com/paper/1906.05082/) (2019)
- [Understanding and Improving Fairness-Accuracy Trade-offs in Multi-Task Learning](https://mlsanity.com/paper/2106.02705/) (2021)
- [Fair Data Adaptation with Quantile Preservation](https://mlsanity.com/paper/1911.06685/) (2019)
- [Taking Advantage of Multitask Learning for Fair Classification](https://mlsanity.com/paper/1810.08683/) (2018)
- [Fair learning with Wasserstein barycenters for non-decomposable performance measures](https://mlsanity.com/paper/2209.00427/) (2022)
- [Rank-Based Multi-task Learning for Fair Regression](https://mlsanity.com/paper/2009.11405/) (2020)
- [Iterative Orthogonal Feature Projection for Diagnosing Bias in Black-Box Models](https://mlsanity.com/paper/1611.04967/) (2016)
- [Learning to Teach Fairness-aware Deep Multi-task Learning](https://mlsanity.com/paper/2206.08403/) (2022)

## Built on by (most cited first, 14 of 14)

- [A Sequentially Fair Mechanism for Multiple Sensitive Attributes](https://mlsanity.com/paper/2309.06627/) (2023)
- [Mitigating Discrimination in Insurance with Wasserstein Barycenters](https://mlsanity.com/paper/2306.12912/) (2023)
- [FairBranch: Mitigating Bias Transfer in Fair Multi-task Learning](https://mlsanity.com/paper/2310.13746/) (2023)
- [Parametric Fairness with Statistical Guarantees](https://mlsanity.com/paper/2310.20508/) (2023)
- [Multi-Output Distributional Fairness via Post-Processing](https://mlsanity.com/paper/2409.00553/) (2024)
- [Geospatial Disparities: A Case Study on Real Estate Prices in Paris](https://mlsanity.com/paper/2401.16197/) (2024)
- [Fairness Explainability using Optimal Transport with Applications in Image Classification](https://mlsanity.com/paper/2308.11090/) (2023)
- [OptiGrad: A Fair and more Efficient Price Elasticity Optimization via a Gradient Based Learning](https://mlsanity.com/paper/2404.10275/) (2024)
- [EquiPy: Sequential Fairness using Optimal Transport in Python](https://mlsanity.com/paper/2503.09866/) (2025)
- [Optimal Transport under Group Fairness Constraints](https://mlsanity.com/paper/2601.07144/) (2026)
- [Fair Regression under Demographic Parity: A Unified Framework](https://mlsanity.com/paper/2601.10623/) (2026)
- [Fair regression under localized demographic parity constraints](https://mlsanity.com/paper/2603.25224/) (2026)
- [Is Fairness Truly Fair? Towards Reliable Lipschitz Fairness in Multi-Task Learning via Fixed-texorpdfstringδdelta Alignment](https://mlsanity.com/paper/2606.10632/) (2026)
- [Fairness in multi-class multi-group classification problems via contextial coherent risk measures](https://mlsanity.com/paper/2608.30223/) (2026)

## Abstract (arXiv)

Algorithmic Fairness is an established field in machine learning that aims to reduce biases in data. Recent advances have proposed various methods to ensure fairness in a univariate environment, where the goal is to de-bias a single task. However, extending fairness to a multi-task setting, where more than one objective is optimised using a shared representation, remains underexplored. To bridge this gap, we develop a method that extends the definition of Strong Demographic Parity to multi-task learning using multi-marginal Wasserstein barycenters. Our approach provides a closed form solution for the optimal fair multi-task predictor including both regression and binary classification tasks. We develop a data-driven estimation procedure for the solution and run numerical experiments on both synthetic and real datasets. The empirical results highlight the practical value of our post-processing methodology in promoting fair decision-making.