Optimal Learning in Fairness-Aware Contextual Bandits

Gengyu Xue, Fan Wang, Feiyu Jiang, Zifeng Zhao, Yi Yu

Mitigating unfair disparities in sequential decision-making is a growing concern in machine learning. We study contextual bandits under a global covariate-based Lipschitz fairness constraint, pioneered by \cite{dwork2012fairness}, requiring individuals with similar contexts to receive similar action distributions. We show that this constraint induces a randomisation region near the decision boundary and explicitly quantify the population level cost of fairness. We further establish a canonical representation of the optimal fair policy, which reduces the fair policy design to a lower-dimensional boundary optimisation problem. We develop a lazy fair greedy algorithm that exploits fairness-induced covariate diversity under continuous contexts, with policy updates computed via finite-dimensional linear programming. For general context distributions, including discrete and mixed contexts, we propose a lazy polyhedral upper confidence bound (UCB) algorithm, whose optimistic optimisation reduces to finitely many linear programs over confidence-set vertices. Both methods satisfy fairness at every round and achieve regret of order $O(\sqrt{T} + T^{(d-2)/(d-1)}{\indc\{d\geq 4\}})$ up to…