# Game of Gradients: Mitigating Irrelevant Clients in Federated Learning

arXiv: https://arxiv.org/abs/2110.12257 · HTML: https://mlsanity.com/paper/2110.12257/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 23 Oct 2021.

## Builds on (most cited first, 17 of 17)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Towards Federated Learning at Scale: System Design](https://mlsanity.com/paper/1902.01046/) (2019)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Differentially Private Federated Learning: A Client Level Perspective](https://mlsanity.com/paper/1712.07557/) (2017)
- [Federated Machine Learning: Concept and Applications](https://mlsanity.com/paper/1902.04885/) (2019)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [On the Convergence of Local Descent Methods in Federated Learning](https://mlsanity.com/paper/1910.14425/) (2019)
- [Iterative Learning with Open-set Noisy Labels](https://mlsanity.com/paper/1804.00092/) (2018)
- [CoCoA: A General Framework for Communication-Efficient Distributed Optimization](https://mlsanity.com/paper/1611.02189/) (2016)
- [Incentive Design for Efficient Federated Learning in Mobile Networks: A Contract Theory Approach](https://mlsanity.com/paper/1905.07479/) (2019)
- [Task Agnostic Robust Learning on Corrupt Outputs by Correlation-Guided Mixture Density Networks](https://mlsanity.com/paper/1805.06431/) (2018)

## Built on by (most cited first, 30 of 35)

- [A Survey on Heterogeneous Federated Learning](https://mlsanity.com/paper/2210.04505/) (2022)
- [Recent Advances on Federated Learning: A Systematic Survey](https://mlsanity.com/paper/2301.01299/) (2023)
- [Advances and Open Challenges in Federated Foundation Models](https://mlsanity.com/paper/2404.15381/) (2024)
- [FedDUAP: Federated Learning with Dynamic Update and Adaptive Pruning Using Shared Data on the Server](https://mlsanity.com/paper/2204.11536/) (2022)
- [Privacy and Fairness in Federated Learning: on the Perspective of Trade-off](https://mlsanity.com/paper/2306.14123/) (2023)
- [Minimax Demographic Group Fairness in Federated Learning](https://mlsanity.com/paper/2201.08304/) (2022)
- [An Efficient Federated Distillation Learning System for Multi-task Time Series Classification](https://mlsanity.com/paper/2201.00011/) (2021)
- [Towards Interpretable Federated Learning](https://mlsanity.com/paper/2302.13473/) (2023)
- [A Snapshot of the Frontiers of Client Selection in Federated Learning](https://mlsanity.com/paper/2210.04607/) (2022)
- [Fair yet Asymptotically Equal Collaborative Learning](https://mlsanity.com/paper/2306.05764/) (2023)
- [A Comprehensive Survey of Federated Transfer Learning: Challenges, Methods and Applications](https://mlsanity.com/paper/2403.01387/) (2024)
- [Long-Short History of Gradients is All You Need: Detecting Malicious and Unreliable Clients in Federated Learning](https://mlsanity.com/paper/2208.10273/) (2022)
- [Greedy Shapley Client Selection for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2312.09108/) (2023)
- [Learnings from Federated Learning in the Real world](https://mlsanity.com/paper/2202.03925/) (2022)
- [Gradient Coreset for Federated Learning](https://mlsanity.com/paper/2401.06989/) (2024)
- [Efficient Federated Learning Using Dynamic Update and Adaptive Pruning with Momentum on Shared Server Data](https://mlsanity.com/paper/2408.05678/) (2024)
- [Mitigating Group Bias in Federated Learning for Heterogeneous Devices](https://mlsanity.com/paper/2309.07085/) (2023)
- [Robust Federated Learning against both Data Heterogeneity and Poisoning Attack via Aggregation Optimization](https://mlsanity.com/paper/2211.05554/) (2022)
- [Exploring Data Redundancy in Real-world Image Classification through Data Selection](https://mlsanity.com/paper/2306.14113/) (2023)
- [Maverick-Aware Shapley Valuation for Client Selection in Federated Learning](https://mlsanity.com/paper/2405.12590/) (2024)
- [A Comprehensive Study of Shapley Value in Data Analytics](https://mlsanity.com/paper/2412.01460/) (2024)
- [Using Cooperative Game Theory to Prune Neural Networks](https://mlsanity.com/paper/2311.10468/) (2023)
- [ROSS: RObust decentralized Stochastic learning based on Shapley values](https://mlsanity.com/paper/2411.00365/) (2024)
- [FLMarket: Enabling Privacy-preserved Pre-training Data Pricing for Federated Learning](https://mlsanity.com/paper/2411.11713/) (2024)
- [FedABC: Attention-Based Client Selection for Federated Learning with Long-Term View](https://mlsanity.com/paper/2507.20871/) (2025)
- [Auditable Homomorphic-based Decentralized Collaborative AI with Attribute-based Differential Privacy](https://mlsanity.com/paper/2403.00023/) (2024)
- [GPFL: A Gradient Projection-Based Client Selection Framework for Efficient Federated Learning](https://mlsanity.com/paper/2403.17833/) (2024)
- [CoAst: Validation-Free Contribution Assessment for Federated Learning based on Cross-Round Valuation](https://mlsanity.com/paper/2409.02495/) (2024)
- [Data Overvaluation Attack and Truthful Data Valuation in Federated Learning](https://mlsanity.com/paper/2502.00494/) (2025)
- [Decoding FL Defenses: Systemization, Pitfalls, and Remedies](https://mlsanity.com/paper/2502.05211/) (2025)

## Abstract (arXiv)

The paradigm of Federated learning (FL) deals with multiple clients participating in collaborative training of a machine learning model under the orchestration of a central server. In this setup, each client's data is private to itself and is not transferable to other clients or the server. Though FL paradigm has received significant interest recently from the research community, the problem of selecting the relevant clients w.r.t. the central server's learning objective is under-explored. We refer to these problems as Federated Relevant Client Selection (FRCS). Because the server doesn't have explicit control over the nature of data possessed by each client, the problem of selecting relevant clients is significantly complex in FL settings. In this paper, we resolve important and related FRCS problems viz., selecting clients with relevant data, detecting clients that possess data relevant to a particular target label, and rectifying corrupted data samples of individual clients. We follow a principled approach to address the above FRCS problems and develop a new federated learning method using the Shapley value concept from cooperative game theory. Towards this end, we propose a cooperative game involving the gradients shared by the clients. Using this game, we compute Shapley values of clients and then present Shapley value based Federated Averaging (S-FedAvg) algorithm that empowers the server to select relevant clients with high probability. S-FedAvg turns out to be critical in designing specific algorithms to address the FRCS problems. We finally conduct a thorough empirical analysis on image classification and speech recognition tasks to show the superior performance of S-FedAvg than the baselines in the context of supervised federated learning settings.