  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.
