Not All Retained Clients Are Equal: Client Selection for Federated Unlearning

Thanh Linh Nguyen; Quoc-Viet Pham

cs.LGOct 22, 2026

Not All Retained Clients Are Equal: Client Selection for Federated Unlearning

Authors: Thanh Linh Nguyen, Quoc-Viet Pham

Organizations: School of Computer Science and Statistics, Trinity College Dublin, Ireland

Abstract

Federated unlearning (FU) aims to remove a designated target client's influence from a trained model without the prohibitive cost of retraining from scratch. Existing methods largely treat unlearning as a post-hoc, stateless operation, overlooking that client influence is path-dependent: contributions made during training, particularly during critical learning periods (CLPs), can have disproportionate and persistent effects. Moreover, knowledge overlap and intermittent client availability make relying on all retained clients inefficient and impractical. We introduce PDF, a path-dependent client-selection framework based on the insight that retained clients are not equally valuable for unlearning. During training, PDF maintains lightweight, target-agnostic, CLP-weighted histories summarizing each client's accumulated update direction and global-model alignment. Upon an unlearning request, these histories identify and rank retained clients that are globally informative yet weakly coupled to the target, enabling retraining-based unlearning with only the top- $k$ clients over a small number of rounds. Experiments on FMNIST, CIFAR-10, and CIFAR-100 under IID and non-IID settings show that PDF achieves effective forgetting and strong retained utility with substantially fewer retained clients. In particular, PDF achieves $0\%$ forgetting accuracy with retraining-like MIA AUC on non-IID CIFAR-10, improves retained accuracy by up to $6.91$ percentage points over the strongest competing FU baseline on CIFAR-100, and reduces communication by approximately $69\%$ and computation by $57$ -- $61\%$ relative to Retrain.

Figures & tables

Figure 2: Illustration of CLP detection using the FGN proxy on FMNIST [ 34 ] , where the green double-headed arrows and triangles indicate the detected CLPs .

Metric	$\alpha$	Retrain	FUSED	CONDA	E-F	FedEraser	FOUL	FedRecovery	GDFA	PDF 0.1	PDF 0.5	PDF 0.9
FMNIST-CNN
FA	0.1	0.44	0.44 ( $+$ 0.00)	0.70 ( $+$ 0.26)	0.56 ( $+$ 0.12)	1.11 ( $+$ 0.67)	0.75 ( $+$ 0.31)	0.60 ( $+$ 0.16)	0.28 ( $-$ 0.16)	0.00 ( $-$ 0.44)	0.72 ( $+$ 0.28)	0.44 ( $+$ 0.00)
FA	1.0	0.92	0.82 ( $-$ 0.10)	0.94 ( $+$ 0.02)	0.45 ( $-$ 0.47)	0.53 ( $-$ 0.39)	0.77 ( $-$ 0.15)	0.87 ( $-$ 0.06)	0.14 ( $-$ 0.78)	0.28 ( $-$ 0.64)	0.28 ( $-$ 0.64)	0.92 ( $+$ 0.00)
RA	0.1	88.20	87.14 ( $-$ 1.06)	85.17 ( $-$ 3.02)	81.89 ( $-$ 6.31)	61.04 ( $-$ 27.16)	85.60 ( $-$ 2.60)	85.22 ( $-$ 2.98)	81.83 ( $-$ 6.37)	82.60 ( $-$ 5.60)	85.97 ( $-$ 2.23)	86.89 ( $-$ 1.31)
RA	1.0	90.45	89.60 ( $-$ 0.85)	89.40 ( $-$ 1.05)	85.94 ( $-$ 4.50)	76.42 ( $-$ 14.03)	89.64 ( $-$ 0.81)	89.64 ( $-$ 0.81)	88.25 ( $-$ 2.20)	89.34 ( $-$ 1.11)	89.35 ( $-$ 1.10)	89.55 ( $-$ 0.90)
MIA AUC	0.1	50.32	50.05 ( $-$ 0.27)	50.11 ( $-$ 0.20)	49.84 ( $-$ 0.48)	49.92 ( $-$ 0.40)	49.71 ( $-$ 0.61)	50.01 ( $-$ 0.31)	50.00 ( $-$ 0.32)	50.01 ( $-$ 0.31)	50.00 ( $-$ 0.32)	49.91 ( $-$ 0.41)

Table 1: Performance comparison between PDF and other FU methods on three datasets under

\alpha\in\{0.1,1.0\}

. Subscripts on PDF denote

\beta\in\{0.1,0.5,0.9\}

, which controls the forgetting–utility trade-off:

0.1

is forgetting-oriented,

0.5

balances forgetting and utility preservation, and

0.9

is utility-preservation-oriented . All variants use

k=25

selected unlearning clients. Values in parentheses are deltas relative to Retrain. For FA, RA, and MIA AUC, red marks the best and green the second-best method across all unlearning methods (Retrain is the reference and is excluded), ranked by FA (

\downarrow

), RA (

\uparrow

), and

|\Delta\mathrm{MIA}|

(

\downarrow

Method	Space Complexity
Retrain	$\mathcal{O}\!\left(P+\|\mathcal{I}_{\mathrm{ret}}\|\cdot P\right)$
FUSED	$\mathcal{O}\!\left(P+\|\mathcal{I}_{\mathrm{ret}}\|\cdot A\right)$
CONDA	$\mathcal{O}\!\left(N\cdot P+P\right)$
E-F	$\mathcal{O}\!\left(T_{\mathrm{learn}}\cdot M\cdot P+P\right)$
FedEraser	$\mathcal{O}\!\left(H\cdot M\cdot P+\|\mathcal{I}_{\mathrm{ret}}\|\cdot P\right)$
FOUL	$\mathcal{O}\!\left(P+N\cdot P+N^{2}\right)$

Table 2: Space complexity analysis.

	$k$	$10$	$15$	$20$	$25$	$30$	$35$
$\beta=0.1$	FA	0.00	0.00	0.00	0.00	0.28	0.28
	RA	75.65	80.51	81.26	82.60	84.45	85.18
	MIA AUC	49.96 ( $-$ 0.36)	50.47 ( $+$ 0.15)	50.09 ( $-$ 0.23)	50.01 ( $-$ 0.31)	50.02 ( $-$ 0.30)	49.95 ( $-$ 0.37)
	Comp	0.76	0.78	0.81	0.83	0.85	0.87
$\beta=0.5$	FA	0.28	0.28	0.28	0.72	0.44	0.28
	RA	79.26	82.76	84.43	85.97	86.40	86.37

Table 3: Ablation study on the number of selected unlearning clients

k

and knowledge retention–forgetting tradeoff

\beta

on FMNIST under

\alpha=0.1

with

\mathcal{I}_{\mathrm{tar}}={0}

. MIA AUC values in parentheses denote differences from Retrain (

50.32

). The shaded column denotes the default

k=25

in Tab. 1 .

FMNIST-CNN (Retrain MIA AUC: 50.32 / 50.23)
	$\alpha=0.1$			$\alpha=1.0$
Method	FA	RA	$\Delta$ MIA	FA	RA	$\Delta$ MIA
PDF	0.72	85.97	$-$ 0.32	0.28	89.35	$+$ 0.02
non-CLP	0.28	85.35	$-$ 0.16	0.43	89.26	$+$ 0.02
Rev	1.36	82.28	$+$ 0.04	1.33	89.14	$-$ 0.06
high-Coh	1.24	82.15	$-$ 0.34	1.23	89.04	$+$ 0.03

Table 4: Ablation of PDF against its selection variants, with

\beta=0.5

\lambda=0.7

, and

k=25

clients selected for unlearning.

\Delta

MIA is the signed deviation of MIA AUC from the retrained reference.

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Open paper AskPDF arXiv

Federated unlearning (FU) enables the removal of specific data contributions from federated learning (FL) models to comply with regulations such as the General Data Protection Regulation (GDPR). However, most existing FU methods are designed for the FedAvg paradigm, where all clients share a single global model. In practice, personalized federated learning (pFL) methods such as FedPer, FedRep, Ditto, and FedBN have become widely adopted due to their superior handling of non-IID data. These methods decompose the model into shared global layers and client-specific personalized layers, fundamentally altering the semantics of unlearning, yet this setting has received little attention. We formalize FU under the pFL paradigm, identifying a tension between unlearning completeness on shared layers and personalization preservation for remaining clients. We then propose pFedUL, a layer-aware selective unlearning framework comprising three components: (1) gradient-based layer-wise contribution attribution that separately quantifies the target client's influence on shared and personalized parameters, (2) adaptive selective unlearning that applies differentiated forgetting strategies across layer types, and (3) a lightweight recalibration protocol enabling remaining clients to restore personalization with minimal overhead. We further introduce two new metrics, Personalization Preservation Score (PPS) and Cross-client Fairness Index (CFI), to evaluate pFL-specific unlearning quality. Experiments on CIFAR-10, CIFAR-100, and FEMNIST under varying non-IID settings indicate that pFedUL achieves unlearning effectiveness comparable to full retraining while maintaining an average of 97.3% personalized accuracy for remaining clients. Compared with six state-of-the-art FU methods adapted to the pFL setting, pFedUL consistently achieves superior personalization preservation.

Abstract

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