Few-for-Many Personalized Federated Learning

Ping Guo; Tiantian Zhang; Xi Lin; Xiang Li; Zhi-Ri Tang; Qingfu Zhang

cs.AIMar 12, 2026

Few-for-Many Personalized Federated Learning

Authors: Ping Guo, Tiantian Zhang, Xi Lin, Xiang Li, Zhi-Ri Tang, Qingfu Zhang

Organizations: City University of Hong Kong · CityU Shenzhen Research Institute · Hong Kong Metropolitan University · Xi’an Jiaotong University ·

Abstract

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.

Figures & tables

Figure 1: Paradigms of Personalized Federated Learning. Left: Centralized methods maintain a single global model for all $M$ clients, failing to capture client heterogeneity. Center: Per-client methods train $M$ independent models, sacrificing collaborative learning benefits and suffering from data scarcity. Right: Our proposed few-for-many approach maintains $K$ server models ( $K\ll M$ ) that collectively serve all clients. Each client selects the best-fitting model, achieving strong personalization while preserving collaboration.

Centralized Methods (Single Global Model)
Method	Pathological heterogeneous setting		Practical heterogeneous setting
	CIFAR-100		FEMNIST	CIFAR-10		CIFAR-100		TINY	AG News
	$M=10$	$M=20$	$M=20$	$M=10$	$M=20$	$M=10$	$M=20$	$M=10$	$M=20$
FedAvg [ 29 ]	$\text{29.00}\pm\text{3.94}$	$\text{28.57}\pm\text{4.37}$	$\text{96.65}\pm\text{1.81}$	$\text{61.36}\pm\text{8.54}$	$\text{61.26}\pm\text{8.64}$	$\text{30.84}\pm\text{2.26}$	$\text{31.10}\pm\text{4.21}$	$\text{13.49}\pm\text{1.55}$	$\text{88.90}\pm\text{7.15}$
FedProx [ 22 ]	$\text{28.56}\pm\text{4.50}$	$\text{28.11}\pm\text{3.86}$	$\text{96.51}\pm\text{2.32}$	$\text{60.87}\pm\text{7.87}$	$\text{61.38}\pm\text{9.35}$	$\text{30.74}\pm\text{2.25}$	$\text{30.90}\pm\text{4.03}$	$\text{13.64}\pm\text{1.56}$	$\text{83.42}\pm\text{11.34}$
FedMTL [ 37 ]	$\text{65.33}\pm\text{3.64}$	$\text{59.65}\pm\text{3.70}$	$\textbf{\text{100.00}}\boldsymbol{\pm}\textbf{\text{0.00}}$	$\text{85.92}\pm\text{11.18}$	$\text{85.75}\pm\text{11.62}$	$\text{46.28}\pm\text{3.82}$	$\text{44.79}\pm\text{5.25}$	$\text{23.49}\pm\text{2.43}$	$\text{94.10}\pm\text{7.56}$

Table 1: Overall performance comparison across CIFAR-10, CIFAR-100, TINY (TinyImageNet), AG News, and FEMNIST datasets under pathological and practical heterogeneous settings. Results are reported as mean accuracy (%)

\pm

standard deviation. Best results are highlighted and bolded , second-best results are underlined .

Figure 3: Mean client accuracy comparison across communication configurations. All configurations achieve comparable mean client accuracy (87.8–88.3%), demonstrating that our method is robust to different communication-computation trade-offs.

Figure 4: Communication-computation trade-off. Convergence of

g^{\text{STCH-Set}}

vs total local updates for different (local epochs, communication rounds) configurations. Local epochs (LE)

\in\{1,2,4,8,16\}

with corresponding communication rounds (GR) to maintain 2000 total updates.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Description
$M$	number of heterogeneous clients
$K$	number of shared models in the K-for-M framework
$L_{i}(\theta)$	expected (population) loss for client $i$ with model $\theta$
$\hat{L}_{i}(\theta)$	empirical loss for client $i$ based on finite samples
$\theta_{i}^{*}$	optimal personalized model for client $i$ , defined as $\arg\min_{\theta}L_{i}(\theta)$
$\Theta^{(K)}_{*}$	optimal K-for-M solution (minimizing population losses)

Appendix

Table 3: Key notation for theoretical analysis. Stars ( ∗ ) denote optimal or population-level quantities, while hats (

\hat{\cdot}

) denote empirical estimators.

Type	Dataset	Model	Rounds	Local Epochs	Batch Size	Learning Rate	Join Ratio
Benchmark	CIFAR-10	CNN	2000	1	50	0.005	1.0
	CIFAR-100	CNN	2000	1	50	0.005	1.0
	TinyImageNet	CNN	2000	1	50	0.0005	1.0
	AG News	TextCNN	2000	1	100	0.005	1.0
	FEMNIST	CNN	2000	1	100	0.005	1.0
Medical	Kvasir	ResNet-18	1000	1	100	0.002	1.0

Appendix

Table 4: Training hyperparameters for benchmark and medical datasets. Benchmark datasets use 2000 rounds with CNN/TextCNN backbones, while medical datasets use 1000 rounds with ResNet-18 to prevent overfitting on smaller institutional samples. All experiments employ single local epoch and full client participation for fair comparison across methods.

Figure 7: Impact of

\mu

on dual-layer weights. (a) Outer weights

\alpha_{i}

distribution across clients. (b) Inner weight entropy (higher = softer selection). (c) Max inner weight (closer to 1 = harder selection). As

\mu\to 0

, FedFew recovers hard clustering like IFCA.

Figure 8: Convergence vs communication rounds. Re-plotting the main paper data against communication rounds instead of total updates reveals the communication efficiency perspective: LE=16 converges in 125 rounds while LE=1 requires 2000 rounds, achieving

16\times

communication reduction with comparable final

g^{\text{STCH-Set}}

values.

	CIFAR-10			CIFAR-100			Medical
Method	Dir-10	Dir-20	Pat-10	Dir-10	Dir-20	Pat-20	Kvasir	FedISIC
FedAvg	0.981	0.981	0.982	0.995	0.982	0.977	0.999	0.945
FedProx	0.984	0.977	0.976	0.995	0.983	0.982	0.981	0.924
APFL	0.992	0.985	0.996	0.995	0.988	0.996	0.994	0.950
Ditto	0.984	0.982	0.997	0.994	0.987	0.996	0.994	0.951
FedRep	0.990	0.985	0.997	0.995	0.991	0.996	0.995	0.938

Appendix

Table 5: Jain’s Fairness Index (higher is better,

J=1

is perfect fairness).

	AG News			Kvasir
$K$	Min	Mean	Max	Min	Mean	Max
1	84.5	96.4	100.0	79.5	91.6	99.5
2	73.8	95.7	100.0	82.4	92.2	99.8
3	83.9	96.0	100.0	83.9	92.9	100.0
4	78.0	95.7	100.0	82.9	92.6	100.0
5	86.3	96.2	100.0	81.2	92.5	100.0

Appendix

Table 6: Test accuracy (%) vs. number of server models

K

on AG News and Kvasir datasets.

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