Metric-Free Individual Fairness in Online Learning

We study an online learning problem subject to the constraint of individual fairness, which requires that similar individuals are treated similarly. Unlike prior work on individual fairness, we do not assume the similarity measure among individuals is known, nor do we assume that such measure takes a certain parametric form. Instead, we leverage the existence of an auditor who detects fairness violations without enunciating the quantitative measure. In each round, the auditor examines the learner's decisions and attempts to identify a pair of individuals that are treated unfairly by the learner. We provide a general reduction framework that reduces online classification in our model to standard online classification, which allows us to leverage existing online learning algorithms to achieve sub-linear regret and number of fairness violations. Surprisingly, in the stochastic setting where the data are drawn independently from a distribution, we are also able to establish PAC-style fairness and accuracy generalization guarantees (Rothblum and Yona [2018] ), despite only having access to a very restricted form of fairness feedback. Our fairness generalization bound qualitatively matches the uniform convergence bound of Rothblum and Yona [2018] , while also providing a meaningful accuracy generalization guarantee. Our results resolve an open question by Gillen et al. [2018] by showing that online learning under an unknown individual fairness constraint is possible even without assuming a strong parametric form of the underlying similarity measure. * Previous versions of this paper included an error in one of the proofs, which was fixed using an additional assumption in the most recent version. In this version, we correct the error without the need for any additional assumptions. However, we achieve slightly slower rates than before. We were also made aware of the connection to the online optimization with long-term constraints literature, and the new related work section discusses some similarities and differences.