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

Mathieu Molina · Nicolas Gast · Patrick Loiseau · Vianney Perchet

Great Hall & Hall B1+B2 (level 1) #1814
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Wed 13 Dec 8:45 a.m. PST — 10:45 a.m. PST

Abstract: We consider the problem of online allocation subject to a long-term fairness penalty. Contrary to existing works, however, we do not assume that the decision-maker observes the protected attributes---which is often unrealistic in practice. Instead they can purchase data that help estimate them from sources of different quality; and hence reduce the fairness penalty at some cost. We model this problem as a multi-armed bandit problem where each arm corresponds to the choice of a data source, coupled with the fair online allocation problem. We propose an algorithm that jointly solves both problems and show that it has a regret bounded by $\mathcal{O}(\sqrt{T})$. A key difficulty is that the rewards received by selecting a source are correlated by the fairness penalty, which leads to a need for randomization (despite a stochastic setting). Our algorithm takes into account contextual information available before the source selection, and can adapt to many different fairness notions.

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