Attack-Resistant Uniform Fairness for Linear and Smooth Contextual Bandits

Abstract

Modern digital platforms use contextual bandits to allocate valuable exposure and opportunities among competing participants. Fair treatment is therefore an important concern, yet reward maximization alone does not ensure that preferential allocation reflects participants' merits. We develop algorithms for linear and smooth contextual bandits under uniform merit-based fairness, requiring the reward ordering to justify preferential allocation across all contexts and rounds, and study how these guarantees are affected by adversarial reward corruption. Our algorithms achieve \((1-\widetilde O(1/T))\)-fairness, with regret that is minimax optimal among fair policies for linear rewards and nearly minimax optimal for smooth rewards. In the linear setting, matching lower bounds identify the price of fairness exactly: minimax regret increases from \(\log T\) to \(\log^2 T\). For smooth rewards, the cost of fairness is at most polylogarithmic. We further establish a separation between regret and fairness robustness: an \(\widetilde O(1)\) corruption budget can cause substantial fairness violations without worsening the regret order. We therefore develop robust algorithms that adapt sampling, estimation, and fairness certification to corruption, which preserve uniform fairness and achieve minimax-optimal and nearly optimal regrets for linear and smooth rewards, respectively. Numerical and semi-synthetic experiments illustrate these findings.