Meritocratic Fairness in Budgeted Combinatorial Multi-armed Bandits via Shapley Values
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arXiv
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| Format: | Preprint |
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2026
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| author | Sharma, Shradha Dhamal, Swapnil Jain, Shweta |
| author_facet | Sharma, Shradha Dhamal, Swapnil Jain, Shweta |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00762 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Meritocratic Fairness in Budgeted Combinatorial Multi-armed Bandits via Shapley Values Sharma, Shradha Dhamal, Swapnil Jain, Shweta Machine Learning Artificial Intelligence Multiagent Systems 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. |
| title | Meritocratic Fairness in Budgeted Combinatorial Multi-armed Bandits via Shapley Values |
| topic | Machine Learning Artificial Intelligence Multiagent Systems |
| url | https://arxiv.org/abs/2605.00762 |