Meritocratic Fairness in Budgeted Combinatorial Multi-armed Bandits via Shapley Values

2026-05-01

AI Summary

This work addresses the challenge of ensuring fairness in full-bandit feedback combinatorial multi-armed bandits, where individual arm contributions are unobservable. To this end, the authors propose the K-Shapley value—a unique extension of the Shapley value under combinatorial constraints—that satisfies symmetry, linearity, null player, and efficiency axioms. Building upon this notion, they design the K-SVFair-FBF algorithm, which simultaneously learns an unknown valuation function and achieves merit-based fairness. Notably, this is the first algorithm to jointly guarantee fairness and robustness to noise under full-bandit feedback. Theoretically, it achieves a fairness regret upper bound of $O(T^{3/4})$. Empirical evaluations demonstrate that K-SVFair-FBF significantly outperforms existing baselines in federated learning and social influence maximization tasks, effectively balancing fairness and utility.

Abstract

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.

Problem

• Meritocratic Fairness
• Budgeted Combinatorial Multi-armed Bandits
• Full-bandit Feedback
• Shapley Values
• Fairness in Bandits

Innovation

• K-Shapley value
• meritocratic fairness
• budgeted combinatorial multi-armed bandits
• full-bandit feedback
• fairness-aware learning