# Demystifying Local and Global Fairness Trade-offs in Federated Learning Using Partial Information Decomposition

arXiv: https://arxiv.org/abs/2307.11333 · HTML: https://mlsanity.com/paper/2307.11333/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 80 references that are in the map.
- First posted on arXiv 21 Jul 2023.

## Builds on (most cited first, 30 of 35)

- [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)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [A Reductions Approach to Fair Classification](https://mlsanity.com/paper/1803.02453/) (2018)
- [Fair Resource Allocation in Federated Learning](https://mlsanity.com/paper/1905.10497/) (2019)
- [Inherent Tradeoffs in Learning Fair Representations](https://mlsanity.com/paper/1906.08386/) (2019)
- [Why Is My Classifier Discriminatory?](https://mlsanity.com/paper/1805.12002/) (2018)
- [FairFed: Enabling Group Fairness in Federated Learning](https://mlsanity.com/paper/2110.00857/) (2021)
- [Fairness-aware Agnostic Federated Learning](https://mlsanity.com/paper/2010.05057/) (2020)
- [Quantifying & Modeling Multimodal Interactions: An Information Decomposition Framework](https://mlsanity.com/paper/2302.12247/) (2023)
- [The Information Bottleneck Problem and Its Applications in Machine Learning](https://mlsanity.com/paper/2004.14941/) (2020)
- [Mitigating Bias in Federated Learning](https://mlsanity.com/paper/2012.02447/) (2020)
- [Addressing Algorithmic Disparity and Performance Inconsistency in Federated Learning](https://mlsanity.com/paper/2108.08435/) (2021)
- [Accuracy and Fairness Trade-offs in Machine Learning: A Stochastic Multi-Objective Approach](https://mlsanity.com/paper/2008.01132/) (2020)
- [Improving Fairness via Federated Learning](https://mlsanity.com/paper/2110.15545/) (2021)
- [Enforcing fairness in private federated learning via the modified method of differential multipliers](https://mlsanity.com/paper/2109.08604/) (2021)
- [R'enyi Fair Inference](https://mlsanity.com/paper/1906.12005/) (2019)
- [Active Fairness Auditing](https://mlsanity.com/paper/2206.08450/) (2022)
- [A Rigorous Information-Theoretic Definition of Redundancy and Relevancy in Feature Selection Based on (Partial) Information Decomposition](https://mlsanity.com/paper/2105.04187/) (2021)
- [Training Fair Models in Federated Learning without Data Privacy Infringement](https://mlsanity.com/paper/2109.05662/) (2021)
- [Causal Feature Selection for Algorithmic Fairness](https://mlsanity.com/paper/2006.06053/) (2020)
- [Minimax Demographic Group Fairness in Federated Learning](https://mlsanity.com/paper/2201.08304/) (2022)
- [Aleatoric and Epistemic Discrimination: Fundamental Limits of Fairness Interventions](https://mlsanity.com/paper/2301.11781/) (2023)
- [Fairness in Supervised Learning: An Information Theoretic Approach](https://mlsanity.com/paper/1801.04378/) (2018)
- [A Novel Approach to the Partial Information Decomposition](https://mlsanity.com/paper/1908.08642/) (2019)
- [Fairness-Aware Neural R'eyni Minimization for Continuous Features](https://mlsanity.com/paper/1911.04929/) (2019)
- [Fairness Under Feature Exemptions: Counterfactual and Observational Measures](https://mlsanity.com/paper/2006.07986/) (2020)
- [To Split or Not to Split: The Impact of Disparate Treatment in Classification](https://mlsanity.com/paper/2002.04788/) (2020)
- [Generating Fair Universal Representations using Adversarial Models](https://mlsanity.com/paper/1910.00411/) (2019)

## Built on by (most cited first, 10 of 10)

- [DiffusionPID: Interpreting Diffusion via Partial Information Decomposition](https://mlsanity.com/paper/2406.05191/) (2024)
- [Quantifying Knowledge Distillation Using Partial Information Decomposition](https://mlsanity.com/paper/2411.07483/) (2024)
- [Intrinsic Fairness-Accuracy Tradeoffs under Equalized Odds](https://mlsanity.com/paper/2405.07393/) (2024)
- [PraFFL: A Preference-Aware Scheme in Fair Federated Learning](https://mlsanity.com/paper/2404.08973/) (2024)
- [A Unified View of Group Fairness Tradeoffs Using Partial Information Decomposition](https://mlsanity.com/paper/2406.04562/) (2024)
- [The Cost of Local and Global Fairness in Federated Learning](https://mlsanity.com/paper/2503.22762/) (2025)
- [CurvFed: Curvature-Aligned Federated Learning for Fairness without Demographics](https://mlsanity.com/paper/2404.19725/) (2024)
- [pFedFair: Towards Optimal Group Fairness-Accuracy Trade-off in Heterogeneous Federated Learning](https://mlsanity.com/paper/2503.14925/) (2025)
- [Learning Invariant Graph Representations Through Redundant Information](https://mlsanity.com/paper/2512.06154/) (2025)
- [Interpreting Reasoning of Large Language Models via Partial Information Decomposition](https://mlsanity.com/paper/2610.00571/) (2026)

## Abstract (arXiv)

This work presents an information-theoretic perspective to group fairness trade-offs in federated learning (FL) with respect to sensitive attributes, such as gender, race, etc. Existing works often focus on either textitglobal fairness (overall disparity of the model across all clients) or textitlocal fairness (disparity of the model at each client), without always considering their trade-offs. There is a lack of understanding regarding the interplay between global and local fairness in FL, particularly under data heterogeneity, and if and when one implies the other. To address this gap, we leverage a body of work in information theory called partial information decomposition (PID), which first identifies three sources of unfairness in FL, namely, textitUnique Disparity, textitRedundant Disparity, and textitMasked Disparity. We demonstrate how these three disparities contribute to global and local fairness using canonical examples. This decomposition helps us derive fundamental limits on the trade-off between global and local fairness, highlighting where they agree or disagree. We introduce the textitAccuracy and Global-Local Fairness Optimality Problem (AGLFOP), a convex optimization that defines the theoretical limits of accuracy and fairness trade-offs, identifying the best possible performance any FL strategy can attain given a dataset and client distribution. We also present experimental results on synthetic datasets and the ADULT dataset to support our theoretical findings.