Meritocratic Fairness for Infinite and Contextual Bandits

We study fairness in linear bandit problems. Starting from the notion of meritocratic fairness introduced in Joseph et al. (2016), we carry out a more refined analysis of a more general problem, achieving better performance guarantees with fewer modelling assumptions on the number and structure of available choices as well as the number selected. We also analyze the previously-unstudied question of fairness in infinite linear bandit problems, obtaining instance-dependent regret upper bounds as well as lower bounds demonstrating that this instance-dependence is necessary. The result is a framework for meritocratic fairness in an online linear setting that is substantially more powerful, general, and realistic than the current state of the art.