# Understanding the Statistical Accuracy-Communication Trade-off in Personalized Federated Learning with Minimax Guarantees

arXiv: https://arxiv.org/abs/2410.08934 · HTML: https://mlsanity.com/paper/2410.08934/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 55 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Builds on (most cited first, 30 of 44)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [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)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [Adaptive Personalized Federated Learning](https://mlsanity.com/paper/2003.13461/) (2020)
- [Think Locally, Act Globally: Federated Learning with Local and Global Representations](https://mlsanity.com/paper/2001.01523/) (2020)
- [Improving Federated Learning Personalization via Model Agnostic Meta Learning](https://mlsanity.com/paper/1909.12488/) (2019)
- [Federated Learning of a Mixture of Global and Local Models](https://mlsanity.com/paper/2002.05516/) (2020)
- [Adaptive Gradient-Based Meta-Learning Methods](https://mlsanity.com/paper/1906.02717/) (2019)
- [Handbook of Convergence Theorems for (Stochastic) Gradient Methods](https://mlsanity.com/paper/2301.11235/) (2023)
- [Heterogeneous Federated Learning: State-of-the-art and Research Challenges](https://mlsanity.com/paper/2307.10616/) (2023)
- [Federated Meta-Learning with Fast Convergence and Efficient Communication](https://mlsanity.com/paper/1802.07876/) (2018)
- [Decentralized Federated Learning: Fundamentals, State of the Art, Frameworks, Trends, and Challenges](https://mlsanity.com/paper/2211.08413/) (2022)
- [Lower Bounds and Optimal Algorithms for Personalized Federated Learning](https://mlsanity.com/paper/2010.02372/) (2020)
- [Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech Recognition](https://mlsanity.com/paper/1402.1128/) (2014)
- [Federated Fine-tuning of Large Language Models under Heterogeneous Tasks and Client Resources](https://mlsanity.com/paper/2402.11505/) (2024)
- [FedPrompt: Communication-Efficient and Privacy Preserving Prompt Tuning in Federated Learning](https://mlsanity.com/paper/2208.12268/) (2022)
- [Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality](https://mlsanity.com/paper/2006.10593/) (2020)
- [Federated Learning: Opportunities and Challenges](https://mlsanity.com/paper/2101.05428/) (2021)
- [Federated Reconstruction: Partially Local Federated Learning](https://mlsanity.com/paper/2102.03448/) (2021)
- [FedBiOT: LLM Local Fine-tuning in Federated Learning without Full Model](https://mlsanity.com/paper/2406.17706/) (2024)
- [Communication-Efficient Adaptive Federated Learning](https://mlsanity.com/paper/2205.02719/) (2022)
- [FedGroup: Efficient Clustered Federated Learning via Decomposed Data-Driven Measure](https://mlsanity.com/paper/2010.06870/) (2020)
- [Efficient Personalized Federated Learning via Sparse Model-Adaptation](https://mlsanity.com/paper/2305.02776/) (2023)
- [Will Bilevel Optimizers Benefit from Loops](https://mlsanity.com/paper/2205.14224/) (2022)
- [Adaptive and Robust Multi-Task Learning](https://mlsanity.com/paper/2202.05250/) (2022)
- [Personalization Improves Privacy-Accuracy Tradeoffs in Federated Learning](https://mlsanity.com/paper/2202.05318/) (2022)
- [FedDiff: Diffusion Model Driven Federated Learning for Multi-Modal and Multi-Clients](https://mlsanity.com/paper/2401.02433/) (2023)

## Built on by (most cited first, 1 of 1)

- [Towards Better Optimization For Listwise Preference in Diffusion Models](https://mlsanity.com/paper/2510.01540/) (2025)

## Abstract (arXiv)

Personalized federated learning (PFL) offers a flexible framework for aggregating information across distributed clients with heterogeneous data. This work considers a personalized federated learning setting that simultaneously learns global and local models. While purely local training has no communication cost, collaborative learning among the clients can leverage shared knowledge to improve statistical accuracy, presenting an accuracy-communication trade-off in personalized federated learning. However, the theoretical analysis of how personalization quantitatively influences sample and algorithmic efficiency and their inherent trade-off is largely unexplored. This paper makes a contribution towards filling this gap, by providing a quantitative characterization of the personalization degree on the tradeoff. The results further offers theoretical insights for choosing the personalization degree. As a side contribution, we establish the minimax optimality in terms of statistical accuracy for a widely studied PFL formulation. The theoretical result is validated on both synthetic and real-world datasets and its generalizability is verified in a non-convex setting.