Achieving Fairness with a Simple Ridge Penalty

Estimating a fair linear regression model subject to a user-defined level of fairness can be achieved by solving a non-convex quadratic programming optimisation problem with quadratic constraints. In this work we propose an alternative, more flexible approach to this task that enforces a user-defined level of fairness by means of a ridge penalty. Our proposal addresses three limitations of the former approach: it produces regression coefficient estimates that are more intuitive to interpret; it is mathematically simpler, with a solution that is partly in closed form; and it is easier to extend beyond linear regression. We evaluate both approaches empirically on five different data sets, and we find that our proposal provides better goodness of fit and better predictive accuracy while being equally effective at achieving the desired fairness level. In addition we highlight a source of bias in the original experimental evaluation of the non-convex quadratic approach, and we discuss how our proposal can be extended to a wide range of models.