Paper Detail
Shradha Sharma, Swapnil Dhamal, Shweta Jain
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.
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@article{sharma2026meritocratic,
title = {Meritocratic Fairness in Budgeted Combinatorial Multi-armed Bandits via Shapley Values},
author = {Shradha Sharma and Swapnil Dhamal and Shweta Jain},
year = {2026},
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 o},
url = {https://arxiv.org/abs/2605.00762},
keywords = {cs.LG, cs.AI, cs.MA},
eprint = {2605.00762},
archiveprefix = {arXiv},
}
{}