  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.
