  Whilst optimal transport (OT) is increasingly being recognized as a powerful
and flexible approach for dealing with fairness issues, current OT fairness
methods are confined to the use of discrete OT. In this paper, we leverage
recent advances from the OT literature to introduce a stochastic-gradient
fairness method based on a dual formulation of continuous OT. We show that this
method gives superior performance to discrete OT methods when little data is
available to solve the OT problem, and similar performance otherwise. We also
show that both continuous and discrete OT methods are able to continually
adjust the model parameters to adapt to different levels of unfairness that
might occur in real-world applications of ML systems.
