Impacts of Individual Fairness on Group Fairness from the Perspective of Generalized Entropy

This paper investigates how the degree of group fairness changes when the degree of individual fairness is actively controlled. As a metric quantifying individual fairness, we consider generalized entropy (GE) recently introduced into machine learning community. To control the degree of individual fairness, we design a classification algorithm satisfying a given degree of individual fairness through an empirical risk minimization (ERM) with a fairness constraint specified in terms of GE. We show the PAC learnability of the fair ERM problem by proving that the true fairness degree does not deviate much from an empirical one with high probability for finite VC dimension if the sample size is big enough. Our experiments show that strengthening individual fairness degree does not always lead to enhancement of group fairness.