# Fairness-Aware Federated Learning with Trajectory Shapley Value

arXiv: https://arxiv.org/abs/2605.30336 · HTML: https://mlsanity.com/paper/2605.30336/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 25 references that are in the map.
- First posted on arXiv 28 May 2026.

## Builds on (most cited first, 14 of 14)

- [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)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [How To Backdoor Federated Learning](https://mlsanity.com/paper/1807.00459/) (2018)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Measure Contribution of Participants in Federated Learning](https://mlsanity.com/paper/1909.08525/) (2019)
- [GTG-Shapley: Efficient and Accurate Participant Contribution Evaluation in Federated Learning](https://mlsanity.com/paper/2109.02053/) (2021)
- [Hierarchical Split Federated Learning: Convergence Analysis and System Optimization](https://mlsanity.com/paper/2412.07197/) (2024)
- [Federated Multi-Agent Deep Reinforcement Learning Approach via Physics-Informed Reward for Multi-Microgrid Energy Management](https://mlsanity.com/paper/2301.00641/) (2022)
- [Beyond ADMM: A Unified Client-variance-reduced Adaptive Federated Learning Framework](https://mlsanity.com/paper/2212.01519/) (2022)
- [FedADMM-InSa: An Inexact and Self-Adaptive ADMM for Federated Learning](https://mlsanity.com/paper/2402.13989/) (2024)
- [On the Volatility of Shapley-Based Contribution Metrics in Federated Learning](https://mlsanity.com/paper/2405.08044/) (2024)
- [A Multi-Objective Optimization framework for Decentralized Learning with coordination constraints](https://mlsanity.com/paper/2507.13983/) (2025)

## Abstract (arXiv)

Federated learning is an emerging distributed paradigm that addresses the challenges posed by heterogeneous, privacy-sensitive data. It enables multiple clients to train a model collaboratively by aggregating their local updates at a server. However, conventional aggregation schemes typically use fixed weights that fail to reflect unequal and time-varying client contributions, leading to biased and unstable learning. To improve fairness and stability, we propose the Trajectory Shapley Value (TSV), a contribution metric that evaluates how each client influences the optimization trajectory of the global model using a validation-based, temporally consistent utility. Building on TSV, we design FedTSV, an adaptive aggregation method that converts per-round evaluations into dynamic client weights, allowing the server to respond to heterogeneous and adversarial participation in real time. Experiments on benchmark datasets show that FedTSV accelerates convergence, improves robustness, and yields more equitable contribution assessments, thereby providing a principled foundation for fairness-aware federated optimization.