Online Learning with an Unknown Fairness Metric

TL;DR

This paper introduces an online learning algorithm for linear contextual bandits that respects unknown fairness constraints, balancing social fairness with reward optimization, and achieves low fairness violations with optimal regret.

Contribution

It presents a novel algorithm that learns an unknown fairness metric from weak feedback while maintaining low fairness violations and optimal regret in adversarial settings.

Findings

Fairness violations grow logarithmically with time

Achieves optimal $O( ootT)$ regret bound

Balances fairness constraints with reward maximization

Abstract

We consider the problem of online learning in the linear contextual bandits setting, but in which there are also strong individual fairness constraints governed by an unknown similarity metric. These constraints demand that we select similar actions or individuals with approximately equal probability (arXiv:1104.3913), which may be at odds with optimizing reward, thus modeling settings where profit and social policy are in tension. We assume we learn about an unknown Mahalanobis similarity metric from only weak feedback that identifies fairness violations, but does not quantify their extent. This is intended to represent the interventions of a regulator who "knows unfairness when he sees it" but nevertheless cannot enunciate a quantitative fairness metric over individuals. Our main result is an algorithm in the adversarial context setting that has a number of fairness violations that depends only logarithmically on $T$, while obtaining an optimal $O(\sqrt{T})$ regret bound to the best fair policy.