Learning Non-Discriminatory Predictors

We consider learning a predictor which is non-discriminatory with respect to a "protected attribute" according to the notion of "equalized odds" proposed by Hardt et al. 2016. We study the problem of learning such a non-discriminatory predictor from a finite training set, both statistically and computationally. We show that a post-hoc correction approach, as suggested by Hardt et al, can be highly suboptimal, present a nearly-optimal statistical procedure, argue that the associated computational problem is intractable, and suggest a second moment relaxation of the non-discrimination definition for which learning is tractable.