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.

翻译：算法公平性是机器学习中一个成熟的领域，旨在减少数据中的偏差。近期研究提出了多种方法以确保单变量环境下的公平性，其目标是消除单一任务的偏差。然而，将公平性扩展到使用共享表示优化多个目标的多任务场景中仍鲜有探索。为填补这一空白，我们开发了一种方法，利用多边际Wasserstein重心将强人口均等性定义扩展到多任务学习。我们的方法为最优公平多任务预测器提供了闭式解，涵盖回归和二元分类任务。我们设计了该解的数据驱动估计程序，并在合成数据集和真实数据集上进行了数值实验。实证结果凸显了我们的后处理方法论在促进公平决策方面的实用价值。