Key Takeaway
You can guarantee merit-based, proportional participation even when you only observe combined group outcomes by estimating restricted Shapley-style contributions; the proposed algorithm drives fairness to improve over time with provable sublinear regret.
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Key Findings
Define each arm’s merit with a Shapley-style value that only considers coalitions up to the allowed team size (K-Shapley). Use repeated sampling and Monte Carlo permutations to estimate those values from only total-group feedback, then pick arms in proportion to their estimated merit. The K-SVFair-FBF algorithm combines optimistic estimates with randomized rounding to ensure arms with uncertain estimates still get opportunities. The method achieves provable sublinear fairness regret and works in practical settings like federated learning and influence maximization while keeping overall performance comparable. Monte Carlo permutations
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Data Highlights
1Fairness regret for the proposed algorithm scales as Õ(T^{3/4} · K · sqrt(M)) — sublinear in time T (so fairness improves with more rounds).
2A simpler baseline that separates exploration and fairness achieves Õ(T^{4/5} · K · M) fairness regret, showing the proposed approach reduces long-run unfairness faster.
3Known lower bound for reward-only learning under full-group feedback is on the order of T^{2/3}, so the T^{3/4} result is close given the extra noise from contribution estimation.
What This Means
Engineers and product leads who must allocate scarce selection slots (clients, seeds, or workers) fairly while only observing group-level outcomes — for example federated learning coordinators and platform designers for influencer campaigns. Researchers building multi-agent systems or fairness-aware selection policies can use the K-Shapley definition and the sampling strategy to enforce proportional, merit-based participation. federated learning
Key Figures
Fig 1: (a) Synthetic Dataset
Fig 2: (a) Synthetic Dataset
Fig 3: (a) R = 250 R=250 and L = 50 L=50
Fig 4: (a) Federated Learning Dataset
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Learn MoreYes, But...
The method assumes a fixed set of arms, a fixed team size K, and stationary (unchanging) reward distributions; it does not yet handle dynamic arrivals or departures. Computing K-Shapley estimates requires Monte Carlo sampling and repeated plays, which increases computation and sample cost compared with reward-only bandits. The theoretical guarantees hinge on bounds like rewards in [0,1] and may degrade if those assumptions fail or if computation budgets force very coarse approximations. Monte Carlo sampling
Full Analysis
The work tackles fair selection when only the total reward of a chosen group is observed (no per-member feedback). It adapts the Shapley value — a principled way to split group payoff among contributors — to a budgeted setting by defining K-Shapley values that average an arm’s marginal contribution across coalitions of size at most K. Because those contributions cannot be observed directly, the algorithm estimates K-Shapley values with Monte Carlo permutations and repeated evaluations to reduce stochastic noise, then uses optimistic upper confidence adjustments so under-explored arms still get chosen. Shapley value concept randomized rounding
K-SVFair-FBF constructs a probabilistic selection vector from optimistic K-Shapley estimates and turns it into an unbiased K-sized subset via randomized rounding. The paper proves the method achieves sublinear fairness regret, formally Õ(T^{3/4} · K · sqrt(M)), which is worse than the theoretical lower bound for reward-only learning (T^{2/3}) but close given the added estimation noise. Experiments in federated learning and influence maximization show the approach yields more balanced participation without sacrificing overall utility. The main trade-offs are additional sampling and computation to estimate contributions and the current limitation to stationary, fixed-arm settings. federated learning
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Credibility Assessment:
Includes an author with h-index 24 (established researcher range) and another with h-index 9; despite being an arXiv preprint, the presence of a higher h-index author and recognized research impact gives stronger credibility.