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 \textit{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：算法公平是机器学习中旨在减少数据偏差的成熟领域。近期研究提出了多种方法以确保单变量环境下的公平性，即针对单一任务进行去偏。然而，将公平性扩展到多任务场景（即使用共享表示优化多个目标）仍是一个尚待充分探索的问题。为弥补这一空白，我们开发了一种方法，通过多边际Wasserstein重心将\textit{强人口均等}的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（涵盖回归与二分类任务）提供了闭式解。我们针对该解开发了数据驱动的估计程序，并在合成数据集与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框架在促进公平决策方面的实用价值。