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We consider the problem of online allocation subject to a long-term fairnesspenalty. Contrary to existing works, however, we do not assume that thedecision-maker observes the protected attributes -- which is often unrealisticin practice. Instead they can purchase data that help estimate them fromsources of different quality; and hence reduce the fairness penalty at somecost. We model this problem as a multi-armed bandit problem where each armcorresponds to the choice of a data source, coupled with the online allocationproblem. We propose an algorithm that jointly solves both problems and showthat it has a regret bounded by $\mathcal{O}(\sqrt{T})$. A key difficulty isthat the rewards received by selecting a source are correlated by the fairnesspenalty, which leads to a need for randomization (despite a stochasticsetting). Our algorithm takes into account contextual information availablebefore the source selection, and can adapt to many different fairness notions.We also show that in some instances, the estimates used can be learned on thefly.

Trading-off price for data quality to achieve fair online allocation