To Pool or Not To Pool: Analyzing the Regularizing Effects of Group-Fair
  Training on Shared Models
Cyrus Cousins I. Elizabeth Kumar Suresh Venkatasubramanian
In fair machine learning, one source of performance disparities between
groups is over-fitting to groups with relatively few training samples. We
derive group-specific bounds on the generalization error of welfare-centric
fair machine learning that benefit from the larger sample size of the majority
group. We do this by considering group-specific Rademacher averages over a
restricted hypothesis class, which contains the family of models likely to
perform well with respect to a fair learning objective (e.g., a power-mean).
Our simulations demonstrate these bounds improve over a naive method, as
expected by theory, with particularly significant improvement for smaller group
sizes.