Paper:
Online Learning with an Unknown Fairness Metric
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 [?], 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( √ T ) regret bound to the best fair policy.

Review:
The authors study the problem of correcting for individual fairness in an adversarial online learning problem when the fairness constraints depend on an unknown similarity metric between the items. This captures the setting in which a quantitative fairness metric over individuals cannot be pre-specified, but is clear a posteriori. The problem is crucial as it the setting of unknown similarities is extremely natural, and keeping the objective separate from the optimization goal seems often appropriate. They show that optimal fair decisions can be efficiently learned, even in this setting that does not have the direct knowledge of the fairness metric. The setting and approach seem appropriate, and the paper opens up many interesting directions for future work.   The discussion of the related work in the supplementary material was great and I think crucial to situate this work -- I hope room can be made in the final version for it in the main body. To this I would just add two additional papers which also deal with different notions of fairness in online learning settings (https://arxiv.org/abs/1707.01875 and https://arxiv.org/abs/1802.08674).