Individual Fairness in Hindsight

The concept of individual fairness (IF) advocates similar treatment of similar individuals to ensure equality in treatment [Dwork et al. 2012]. In this paper, we extend this notion to account for the time at which a decision is made, in settings where there exists a notion of conduciveness of decisions as perceived by the affected individuals. We introduce two definitions: (i) fairness-across-time (FT) and (ii) fairness-in-hindsight (FH). FT is the simplest temporal extension of IF where treatment of individuals is required to be individually fair relative to the past as well as future, while in FH, we require a one-sided notion of individual fairness that is defined relative to only the past decisions. These two definitions can have drastically different implications in the setting where the principal needs to learn the utility model. We show that linear regret is inevitable under fairness-across-time for non-trivial examples. On the other hand, we design a new algorithm: Cautious Fair Exploration (CaFE), that achieves order-optimal sub-linear regret guarantees under the fairness-in-hindsight constraint for a broad range of settings.