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

TL;DR

This paper addresses online allocation with fairness constraints without observing protected attributes, proposing a bandit-based approach that balances data acquisition costs and fairness, achieving sublinear regret.

Contribution

It introduces a novel algorithm that jointly optimizes data source selection and online allocation under fairness constraints without protected attribute observations.

Findings

Regret bounded by 

Algorithm adapts to various fairness notions

Estimates can be learned on the fly in some cases

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 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. We also show that in some instances, the estimates used can be learned on the fly.