# Few-for-Many Personalized Federated Learning

arXiv: https://arxiv.org/abs/2603.11992 · HTML: https://mlsanity.com/paper/2603.11992/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 44 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Federated Multi-Task Learning](https://mlsanity.com/paper/1705.10467/) (2017)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [FedBN: Federated Learning on Non-IID Features via Local Batch Normalization](https://mlsanity.com/paper/2102.07623/) (2021)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [An Efficient Framework for Clustered Federated Learning](https://mlsanity.com/paper/2006.04088/) (2020)
- [Clustered Federated Learning: Model-Agnostic Distributed Multi-Task Optimization under Privacy Constraints](https://mlsanity.com/paper/1910.01991/) (2019)
- [A Survey on Federated Learning Systems: Vision, Hype and Reality for Data Privacy and Protection](https://mlsanity.com/paper/1907.09693/) (2019)
- [Adaptive Personalized Federated Learning](https://mlsanity.com/paper/2003.13461/) (2020)
- [FedDG: Federated Domain Generalization on Medical Image Segmentation via Episodic Learning in Continuous Frequency Space](https://mlsanity.com/paper/2103.06030/) (2021)
- [Personalized Cross-Silo Federated Learning on Non-IID Data](https://mlsanity.com/paper/2007.03797/) (2020)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Personalized Federated Learning with First Order Model Optimization](https://mlsanity.com/paper/2012.08565/) (2020)
- [FedBABU: Towards Enhanced Representation for Federated Image Classification](https://mlsanity.com/paper/2106.06042/) (2021)
- [FLamby: Datasets and Benchmarks for Cross-Silo Federated Learning in Realistic Healthcare Settings](https://mlsanity.com/paper/2210.04620/) (2022)
- [Multi-Center Federated Learning: Clients Clustering for Better Personalization](https://mlsanity.com/paper/2108.08647/) (2021)
- [Multi-institutional Collaborations for Improving Deep Learning-based Magnetic Resonance Image Reconstruction Using Federated Learning](https://mlsanity.com/paper/2103.02148/) (2021)
- [Federated Learning Meets Multi-objective Optimization](https://mlsanity.com/paper/2006.11489/) (2020)
- [FedSoft: Soft Clustered Federated Learning with Proximal Local Updating](https://mlsanity.com/paper/2112.06053/) (2021)
- [Efficient Distribution Similarity Identification in Clustered Federated Learning via Principal Angles Between Client Data Subspaces](https://mlsanity.com/paper/2209.10526/) (2022)
- [Personalized Federated Learning with Adaptive Batchnorm for Healthcare](https://mlsanity.com/paper/2112.00734/) (2021)

## Built on by (most cited first, 2 of 2)

- [Collaborative Personalized Preference Alignment for LLMs under Data Deficiency](https://mlsanity.com/paper/2610.05898/) (2026)
- [Few-for-Many Best-Arm Identification in Multi-Objective Bandits](https://mlsanity.com/paper/2610.16840/) (2026)

## Abstract (arXiv)

Personalized Federated Learning (PFL) aims to train customized models for clients with highly heterogeneous data distributions while preserving data privacy. Existing approaches often rely on heuristics like clustering or model interpolation, which lack principled mechanisms for balancing heterogeneous client objectives. Serving M clients with distinct data distributions is inherently a multi-objective optimization problem, where achieving optimal personalization ideally requires M distinct models on the Pareto front. However, maintaining M separate models poses significant scalability challenges in federated settings with hundreds or thousands of clients. To address this challenge, we reformulate PFL as a few-for-many optimization problem that maintains only K shared server models (K ll M) to collectively serve all M clients. We prove that this framework achieves near-optimal personalization: the approximation error diminishes as K increases and each client's model converges to each client's optimum as data grows. Building on this reformulation, we propose FedFew, a practical algorithm that jointly optimizes the K server models through efficient gradient-based updates. Unlike clustering-based approaches that require manual client partitioning or interpolation-based methods that demand careful hyperparameter tuning, FedFew automatically discovers the optimal model diversity through its optimization process. Experiments across vision, NLP, and real-world medical imaging datasets demonstrate that FedFew, with just 3 models, consistently outperforms other state-of-the-art approaches. Code is available at https://github.com/pgg3/FedFew.