  This paper studies a parametric family of algorithmic fairness metrics,
called generalized entropy, which originally has been used in public welfare
and recently introduced to machine learning community. As a meaningful metric
to evaluate algorithmic fairness, it requires that generalized entropy specify
fairness requirements of a classification problem and the fairness requirements
should be realized with small deviation by an algorithm. We investigate the
role of generalized entropy as a design parameter for fair classification
algorithm through a fair empirical risk minimization with a constraint
specified in terms of generalized entropy. We theoretically and experimentally
study learnability of the problem.
