  In this work, we develop a novel fairness learning approach for multi-task
regression models based on a biased training dataset, using a popular
rank-based non-parametric independence test, i.e., Mann Whitney U statistic,
for measuring the dependency between target variable and protected variables.
To solve this learning problem efficiently, we first reformulate the problem as
a new non-convex optimization problem, in which a non-convex constraint is
defined based on group-wise ranking functions of individual objects. We then
develop an efficient model-training algorithm based on the framework of
non-convex alternating direction method of multipliers (NC-ADMM), in which one
of the main challenges is to implement an efficient projection oracle to the
preceding non-convex set defined based on ranking functions. Through the
extensive experiments on both synthetic and real-world datasets, we validated
the out-performance of our new approach against several state-of-the-art
competitive methods on several popular metrics relevant to fairness learning.
