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.

本文研究线性 bandit 问题中的公平性，提出 meritocratic 公平的概念，并在更广泛的问题上进行分析，得出更好的性能保证。同时，探讨了无限线性 bandit 问题中的公平性问题，证明了实例相关性是必要的。结果是一个在线线性环境中 meritocratic 公平的框架，比现有技术的研究更强大、更普遍和更现实。