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# Probably Approximately Metric-Fair Learning

*Proceedings of the 35th International Conference on Machine Learning*, PMLR 80:5680-5688, 2018.

#### Abstract

The seminal work of Dwork

*et al.*[ITCS 2012] introduced a metric-based notion of individual fairness: given a task-specific similarity metric, their notion required that every pair of similar individuals should be treated similarly. In the context of machine learning, however, individual fairness does not generalize from a training set to the underlying population. We show that this can lead to computational intractability even for simple fair-learning tasks. With this motivation in mind, we introduce and study a relaxed notion of*approximate metric-fairness*: for a random pair of individuals sampled from the population, with all but a small probability of error, if they are similar then they should be treated similarly. We formalize the goal of achieving approximate metric-fairness simultaneously with best-possible accuracy as Probably Approximately Correct and Fair (PACF) Learning. We show that approximate metric-fairness*does*generalize, and leverage these generalization guarantees to construct polynomial-time PACF learning algorithms for the classes of linear and logistic predictors.