# Loss Gap Parity for Fairness in Heterogeneous Federated Learning

arXiv: https://arxiv.org/abs/2603.29818 · HTML: https://mlsanity.com/paper/2603.29818/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 27 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Builds on (most cited first, 4 of 4)

- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [A Field Guide to Federated Optimization](https://mlsanity.com/paper/2107.06917/) (2021)
- [Gradient Descent on Logistic Regression with Non-Separable Data and Large Step Sizes](https://mlsanity.com/paper/2406.05033/) (2024)
- [Achieving Distributive Justice in Federated Learning via Uncertainty Quantification](https://mlsanity.com/paper/2504.15924/) (2025)

## Abstract (arXiv)

While clients may join federated learning to improve performance on data they rarely observe locally, they often remain self-interested, expecting the global model to perform well on their own data. This motivates an objective that ensures all clients achieve a similar loss gap -the difference in performance between the global model and the best model they could train using only their local data-. To this end, we propose EAGLE, a novel federated learning algorithm that explicitly regularizes the global model to minimize disparities in loss gaps across clients. Our approach is particularly effective in heterogeneous settings, where the optimal local models of the clients may be misaligned. Unlike existing methods that encourage loss parity, potentially degrading performance for many clients, EAGLE targets fairness in relative improvements. We provide theoretical convergence guarantees for EAGLE under non-convex loss functions, and characterize how its iterates perform relative to the standard federated learning objective using a novel heterogeneity measure. Empirically, we demonstrate that EAGLE reduces the disparity in loss gaps among clients by prioritizing those furthest from their local optimal loss, while maintaining competitive utility in both convex and non-convex cases compared to strong baselines.