# Models of fairness in federated learning

arXiv: https://arxiv.org/abs/2112.00818 · HTML: https://mlsanity.com/paper/2112.00818/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 46 references that are in the map.
- First posted on arXiv 1 Dec 2021.

## Builds on (most cited first, 23 of 23)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Agnostic Federated Learning](https://mlsanity.com/paper/1902.00146/) (2019)
- [Fair Resource Allocation in Federated Learning](https://mlsanity.com/paper/1905.10497/) (2019)
- [Collaborative Fairness in Federated Learning](https://mlsanity.com/paper/2008.12161/) (2020)
- [Fairness-aware Agnostic Federated Learning](https://mlsanity.com/paper/2010.05057/) (2020)
- [Model-sharing Games: Analyzing Federated Learning Under Voluntary Participation](https://mlsanity.com/paper/2010.00753/) (2020)
- [Mitigating Bias in Federated Learning](https://mlsanity.com/paper/2012.02447/) (2020)
- [Incentive Mechanisms for Federated Learning: From Economic and Game Theoretic Perspective](https://mlsanity.com/paper/2111.11850/) (2021)
- [Optimality and Stability in Federated Learning: A Game-theoretic Approach](https://mlsanity.com/paper/2106.09580/) (2021)
- [One for One, or All for All: Equilibria and Optimality of Collaboration in Federated Learning](https://mlsanity.com/paper/2103.03228/) (2021)
- [Improving Fairness via Federated Learning](https://mlsanity.com/paper/2110.15545/) (2021)
- [Representation Matters: Assessing the Importance of Subgroup Allocations in Training Data](https://mlsanity.com/paper/2103.03399/) (2021)
- [Hierarchically Fair Federated Learning](https://mlsanity.com/paper/2004.10386/) (2020)
- [Improving Fairness for Data Valuation in Horizontal Federated Learning](https://mlsanity.com/paper/2109.09046/) (2021)
- [Unified Group Fairness on Federated Learning](https://mlsanity.com/paper/2111.04986/) (2021)
- [Federating for Learning Group Fair Models](https://mlsanity.com/paper/2110.01999/) (2021)
- [Incentive Mechanism Design for Federated Learning: Hedonic Game Approach](https://mlsanity.com/paper/2101.09673/) (2021)
- [Optimal Model Averaging: Towards Personalized Collaborative Learning](https://mlsanity.com/paper/2110.12946/) (2021)
- [Data Cooperatives: Towards a Foundation for Decentralized Personal Data Management](https://mlsanity.com/paper/1905.08819/) (2019)

## Built on by (most cited first, 8 of 8)

- [Evaluating and Incentivizing Diverse Data Contributions in Collaborative Learning](https://mlsanity.com/paper/2306.05592/) (2023)
- [FOCUS: Fairness via Agent-Awareness for Federated Learning on Heterogeneous Data](https://mlsanity.com/paper/2207.10265/) (2022)
- [Incentivized Communication for Federated Bandits](https://mlsanity.com/paper/2309.11702/) (2023)
- [Incentivized Truthful Communication for Federated Bandits](https://mlsanity.com/paper/2402.04485/) (2024)
- [Achieving Distributive Justice in Federated Learning via Uncertainty Quantification](https://mlsanity.com/paper/2504.15924/) (2025)
- [Federated Learning as a Network Effects Game](https://mlsanity.com/paper/2302.08533/) (2023)
- [Incentivized Collaboration in Active Learning](https://mlsanity.com/paper/2311.00260/) (2023)
- [Data Quality in Edge Machine Learning: A State-of-the-Art Survey](https://mlsanity.com/paper/2406.02600/) (2024)

## Abstract (arXiv)

In many real-world situations, data is distributed across multiple self-interested agents. These agents can collaborate to build a machine learning model based on data from multiple agents, potentially reducing the error each experiences. However, sharing models in this way raises questions of fairness: to what extent can the error experienced by one agent be significantly lower than the error experienced by another agent in the same coalition? In this work, we consider two notions of fairness that each may be appropriate in different circumstances: "egalitarian fairness" (which aims to bound how dissimilar error rates can be) and "proportional fairness" (which aims to reward players for contributing more data). We similarly consider two common methods of model aggregation, one where a single model is created for all agents (uniform), and one where an individualized model is created for each agent. For egalitarian fairness, we obtain a tight multiplicative bound on how widely error rates can diverge between agents collaborating (which holds for both aggregation methods). For proportional fairness, we show that the individualized aggregation method always gives a small player error that is upper bounded by proportionality. For uniform aggregation, we show that this upper bound is guaranteed for any individually rational coalition (where no player wishes to leave to do local learning).