  Training a classifier under fairness constraints has gotten increasing
attention in the machine learning community thanks to moral, legal, and
business reasons. However, several recent works addressing algorithmic fairness
have only focused on simple models such as logistic regression or support
vector machines due to non-convex and non-differentiable fairness criteria
across protected groups, such as race or gender. Neural networks, the most
widely used models for classification nowadays, are precluded and lack
theoretical guarantees. This paper aims to fill this missing but crucial part
of the literature of algorithmic fairness for neural networks. In particular,
we show that overparametrized neural networks could meet the fairness
constraints. The key ingredient of building a fair neural network classifier is
establishing no-regret analysis for neural networks in the overparameterization
regime, which may be of independent interest in the online learning of neural
networks and related applications.
