Online Learning with an Unknown Fairness Metric
This addresses the challenge of integrating fairness into online decision-making for scenarios like social policy, where regulators can detect but not quantify unfairness, though it is incremental in combining existing bandit and fairness frameworks.
The paper tackles the problem of online learning with linear contextual bandits under unknown fairness constraints, where actions must be selected with approximately equal probability for similar individuals, balancing reward optimization against fairness. The result is an algorithm that achieves an optimal O(√T) regret bound while limiting fairness violations to a logarithmic dependence on T.
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.