# Collaboration Equilibrium in Federated Learning

arXiv: https://arxiv.org/abs/2108.07926 · HTML: https://mlsanity.com/paper/2108.07926/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 45 references that are in the map.
- First posted on arXiv 18 Aug 2021.

## Builds on (most cited first, 27 of 27)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [Taskonomy: Disentangling Task Transfer Learning](https://mlsanity.com/paper/1804.08328/) (2018)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [Clustered Federated Learning: Model-Agnostic Distributed Multi-Task Optimization under Privacy Constraints](https://mlsanity.com/paper/1910.01991/) (2019)
- [Agnostic Federated Learning](https://mlsanity.com/paper/1902.00146/) (2019)
- [Fair Resource Allocation in Federated Learning](https://mlsanity.com/paper/1905.10497/) (2019)
- [Which Tasks Should Be Learned Together in Multi-task Learning?](https://mlsanity.com/paper/1905.07553/) (2019)
- [Think Locally, Act Globally: Federated Learning with Local and Global Representations](https://mlsanity.com/paper/2001.01523/) (2020)
- [Three Approaches for Personalization with Applications to Federated Learning](https://mlsanity.com/paper/2002.10619/) (2020)
- [Personalized Federated Learning: A Meta-Learning Approach](https://mlsanity.com/paper/2002.07948/) (2020)
- [Characterizing and Avoiding Negative Transfer](https://mlsanity.com/paper/1811.09751/) (2018)
- [Personalized Federated Learning using Hypernetworks](https://mlsanity.com/paper/2103.04628/) (2021)
- [Personalized Federated Learning with First Order Model Optimization](https://mlsanity.com/paper/2012.08565/) (2020)
- [UberNet: Training a `Universal' Convolutional Neural Network for Low-, Mid-, and High-Level Vision using Diverse Datasets and Limited Memory](https://mlsanity.com/paper/1609.02132/) (2016)
- [Survey of Personalization Techniques for Federated Learning](https://mlsanity.com/paper/2003.08673/) (2020)
- [Learning the Pareto Front with Hypernetworks](https://mlsanity.com/paper/2010.04104/) (2020)
- [Distributionally Robust Federated Averaging](https://mlsanity.com/paper/2102.12660/) (2021)
- [Robust Federated Learning: The Case of Affine Distribution Shifts](https://mlsanity.com/paper/2006.08907/) (2020)
- [Fully-adaptive Feature Sharing in Multi-Task Networks with Applications in Person Attribute Classification](https://mlsanity.com/paper/1611.05377/) (2016)
- [Model-sharing Games: Analyzing Federated Learning Under Voluntary Participation](https://mlsanity.com/paper/2010.00753/) (2020)
- [Optimality and Stability in Federated Learning: A Game-theoretic Approach](https://mlsanity.com/paper/2106.09580/) (2021)
- [Explaining Algorithmic Fairness Through Fairness-Aware Causal Path Decomposition](https://mlsanity.com/paper/2108.05335/) (2021)
- [Towards Model-Agnostic Post-Hoc Adjustment for Balancing Ranking Fairness and Algorithm Utility](https://mlsanity.com/paper/2006.08267/) (2020)
- [A Wasserstein Minimax Framework for Mixed Linear Regression](https://mlsanity.com/paper/2106.07537/) (2021)

## Built on by (most cited first, 16 of 16)

- [Federated Continual Learning via Knowledge Fusion: A Survey](https://mlsanity.com/paper/2312.16475/) (2023)
- [Vertical Federated Learning: A Structured Literature Review](https://mlsanity.com/paper/2212.00622/) (2022)
- [Find Your Friends: Personalized Federated Learning with the Right Collaborators](https://mlsanity.com/paper/2210.06597/) (2022)
- [Patchwork Learning: A Paradigm Towards Integrative Analysis across Diverse Biomedical Data Sources](https://mlsanity.com/paper/2305.06217/) (2023)
- [Free-Rider and Conflict Aware Collaboration Formation for Cross-Silo Federated Learning](https://mlsanity.com/paper/2410.19321/) (2024)
- [Balancing Similarity and Complementarity for Federated Learning](https://mlsanity.com/paper/2405.09892/) (2024)
- [Benchmarking Data Heterogeneity Evaluation Approaches for Personalized Federated Learning](https://mlsanity.com/paper/2410.07286/) (2024)
- [Decentralized Dynamic Cooperation of Personalized Models for Federated Continual Learning](https://mlsanity.com/paper/2509.23683/) (2025)
- [Leveraging The Edge-to-Cloud Continuum for Scalable Machine Learning on Decentralized Data](https://mlsanity.com/paper/2306.10848/) (2023)
- [United We Defend: Collaborative Membership Inference Defenses in Federated Learning](https://mlsanity.com/paper/2601.06866/) (2026)
- [Adaptive Guidance for Local Training in Heterogeneous Federated Learning](https://mlsanity.com/paper/2410.06490/) (2024)
- [Voronoi-grid-based Pareto Front Learning and Its Application to Collaborative Federated Learning](https://mlsanity.com/paper/2505.20648/) (2025)
- [Learning to Collaborate Over Graphs: A Selective Federated Multi-Task Learning Approach](https://mlsanity.com/paper/2506.10102/) (2025)
- [Incentivizing High-quality Participation From Federated Learning Agents](https://mlsanity.com/paper/2506.16731/) (2025)
- [Federated Learning at the Forefront of Fairness: A Multifaceted Perspective](https://mlsanity.com/paper/2602.00718/) (2026)
- [Adaptive Personalized Federated Learning via Multi-task Averaging of Kernel Mean Embeddings](https://mlsanity.com/paper/2603.02233/) (2026)

## Abstract (arXiv)

Federated learning (FL) refers to the paradigm of learning models over a collaborative research network involving multiple clients without sacrificing privacy. Recently, there have been rising concerns on the distributional discrepancies across different clients, which could even cause counterproductive consequences when collaborating with others. While it is not necessarily that collaborating with all clients will achieve the best performance, in this paper, we study a rational collaboration called ``collaboration equilibrium'' (CE), where smaller collaboration coalitions are formed. Each client collaborates with certain members who maximally improve the model learning and isolates the others who make little contribution. We propose the concept of benefit graph which describes how each client can benefit from collaborating with other clients and advance a Pareto optimization approach to identify the optimal collaborators. Then we theoretically prove that we can reach a CE from the benefit graph through an iterative graph operation. Our framework provides a new way of setting up collaborations in a research network. Experiments on both synthetic and real world data sets are provided to demonstrate the effectiveness of our method.