A Fair Empirical Risk Minimization with Generalized Entropy

Recently a parametric family of fairness metrics to quantify algorithmic fairness has been proposed based on generalized entropy which have been originally used in economics and public welfare. Since these metrics have several advantages such as quantifying unfairness at the individual-level and group-level, and unfold trade-off between the individual fairness and group-level fairness, algorithmic fairness requirement may be given in terms of generalized entropy for a fair classification problem. We consider a fair empirical risk minimization with a fairness constraint specified by generalized entropy. We theoretically investigate if the fair empirical fair classification problem is learnable and how to find an approximate optimal classifier of it.