# Is Shapley Value fair? Improving Client Selection for Mavericks in Federated Learning

arXiv: https://arxiv.org/abs/2106.10734 · HTML: https://mlsanity.com/paper/2106.10734/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 20 Jun 2021.

## Builds on (most cited first, 25 of 25)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Federated Learning on Non-IID Data Silos: An Experimental Study](https://mlsanity.com/paper/2102.02079/) (2021)
- [An Efficient Framework for Clustered Federated Learning](https://mlsanity.com/paper/2006.04088/) (2020)
- [Client Selection for Federated Learning with Heterogeneous Resources in Mobile Edge](https://mlsanity.com/paper/1804.08333/) (2018)
- [Attack of the Tails: Yes, You Really Can Backdoor Federated Learning](https://mlsanity.com/paper/2007.05084/) (2020)
- [Data Poisoning Attacks Against Federated Learning Systems](https://mlsanity.com/paper/2007.08432/) (2020)
- [Client Selection in Federated Learning: Convergence Analysis and Power-of-Choice Selection Strategies](https://mlsanity.com/paper/2010.01243/) (2020)
- [A Principled Approach to Data Valuation for Federated Learning](https://mlsanity.com/paper/2009.06192/) (2020)
- [Lower Bounds and Optimal Algorithms for Personalized Federated Learning](https://mlsanity.com/paper/2010.02372/) (2020)
- [Distributionally Robust Federated Averaging](https://mlsanity.com/paper/2102.12660/) (2021)
- [Client Selection and Bandwidth Allocation in Wireless Federated Learning Networks: A Long-Term Perspective](https://mlsanity.com/paper/2004.04314/) (2020)
- [Robust Federated Learning: The Case of Affine Distribution Shifts](https://mlsanity.com/paper/2006.08907/) (2020)
- [TiFL: A Tier-based Federated Learning System](https://mlsanity.com/paper/2001.09249/) (2020)
- [Measure Contribution of Participants in Federated Learning](https://mlsanity.com/paper/1909.08525/) (2019)
- [Collaborative Machine Learning with Incentive-Aware Model Rewards](https://mlsanity.com/paper/2010.12797/) (2020)
- [Active Federated Learning](https://mlsanity.com/paper/1909.12641/) (2019)
- [An Efficiency-boosting Client Selection Scheme for Federated Learning with Fairness Guarantee](https://mlsanity.com/paper/2011.01783/) (2020)
- [FedCoin: A Peer-to-Peer Payment System for Federated Learning](https://mlsanity.com/paper/2002.11711/) (2020)
- [Hierarchically Fair Federated Learning](https://mlsanity.com/paper/2004.10386/) (2020)
- [Rewarding High-Quality Data via Influence Functions](https://mlsanity.com/paper/1908.11598/) (2019)

## Built on by (most cited first, 7 of 7)

- [Resource-Efficient Federated Learning](https://mlsanity.com/paper/2111.01108/) (2021)
- [Greedy Shapley Client Selection for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2312.09108/) (2023)
- [A Comprehensive Study of Shapley Value in Data Analytics](https://mlsanity.com/paper/2412.01460/) (2024)
- [Data valuation: The partial ordinal Shapley value for machine learning](https://mlsanity.com/paper/2305.01660/) (2023)
- [On the Fragility of Contribution Score Computation in Federated Learning](https://mlsanity.com/paper/2509.19921/) (2025)
- [Photon: Federated LLM Pre-Training](https://mlsanity.com/paper/2411.02908/) (2024)
- [Owen Sampling Accelerates Contribution Estimation in Federated Learning](https://mlsanity.com/paper/2508.21261/) (2025)

## Abstract (arXiv)

Shapley Value is commonly adopted to measure and incentivize client participation in federated learning. In this paper, we show -- theoretically and through simulations -- that Shapley Value underestimates the contribution of a common type of client: the Maverick. Mavericks are clients that differ both in data distribution and data quantity and can be the sole owners of certain types of data. Selecting the right clients at the right moment is important for federated learning to reduce convergence times and improve accuracy. We propose FedEMD, an adaptive client selection strategy based on the Wasserstein distance between the local and global data distributions. As FedEMD adapts the selection probability such that Mavericks are preferably selected when the model benefits from improvement on rare classes, it consistently ensures the fast convergence in the presence of different types of Mavericks. Compared to existing strategies, including Shapley Value-based ones, FedEMD improves the convergence of neural network classifiers by at least 26.9% for FedAvg aggregation compared with the state of the art.