We propose a new framework for meritocratic fairness in budgeted combinatorial multi-armed bandits with full-bandit feedback (BCMAB-FBF). Unlike semi-bandit feedback, the contribution of individual arms is not received in full-bandit feedback, making the setting significantly more challenging. To compute arm contributions in BCMAB-FBF, we first extend the Shapley value, a classical solution concept from cooperative game theory, to the $K$-Shapley value, which captures the marginal contribution of an agent restricted to a set of size at most $K$. We show that $K$-Shapley value is a unique solution concept that satisfies Symmetry, Linearity, Null player, and efficiency properties. We next propose K-SVFair-FBF, a fairness-aware bandit algorithm that adaptively estimates $K$-Shapley value with unknown valuation function. Unlike standard bandit literature on full bandit feedback, K-SVFair-FBF not only learns the valuation function under full feedback setting but also mitigates the noise arising from Monte Carlo approximations. Theoretically, we prove that K-SVFair-FBF achieves $O(T^{3/4})$ regret bound on fairness regret. Through experiments on federated learning and social influence maximization datasets, we demonstrate that our approach achieves fairness and performs more effectively than existing baselines.

翻译：我们提出了一种新的精英公平性框架，适用于全波段反馈下的预算组合多臂老虎机（BCMAB-FBF）。与半波段反馈不同，全波段反馈下个体臂的贡献无法直接获取，这使得该场景更具挑战性。为计算BCMAB-FBF中的臂贡献，我们首先将合作博弈论中的经典解概念——夏普利值扩展为$K$-夏普利值，该值衡量代理在大小不超过$K$的集合中的边际贡献。我们证明$K$-夏普利值是唯一满足对称性、线性性、零玩家及效率性质的解概念。随后提出K-SVFair-FBF算法，该算法能通过未知估值函数自适应地估计$K$-夏普利值。与标准全波段反馈博彩文献不同，K-SVFair-FBF不仅能在全反馈设置下学习估值函数，还能减轻蒙特卡洛近似引入的噪声。理论上，我们证明K-SVFair-FBF在公平性遗憾上可达到$O(T^{3/4})$的后悔界。通过联邦学习和社会影响力最大化数据集上的实验，我们表明该方法能实现公平性且性能优于现有基线方法。