  In this paper, we study the prediction of a real-valued target, such as a
risk score or recidivism rate, while guaranteeing a quantitative notion of
fairness with respect to a protected attribute such as gender or race. We call
this class of problems \emph{fair regression}. We propose general schemes for
fair regression under two notions of fairness: (1) statistical parity, which
asks that the prediction be statistically independent of the protected
attribute, and (2) bounded group loss, which asks that the prediction error
restricted to any protected group remain below some pre-determined level. While
we only study these two notions of fairness, our schemes are applicable to
arbitrary Lipschitz-continuous losses, and so they encompass least-squares
regression, logistic regression, quantile regression, and many other tasks. Our
schemes only require access to standard risk minimization algorithms (such as
standard classification or least-squares regression) while providing
theoretical guarantees on the optimality and fairness of the obtained
solutions. In addition to analyzing theoretical properties of our schemes, we
empirically demonstrate their ability to uncover fairness--accuracy frontiers
on several standard datasets.
