基于Fisher信息矩阵的自适应聚合与客户端协同优化的个性化联邦学习方法

蒋伟进; 刘志华; 崔新雨; 许宇胜; 陈伸有; 胡佳龙

doi:10.11999/JEIT260344

基于Fisher信息矩阵的自适应聚合与客户端协同优化的个性化联邦学习方法

doi: 10.11999/JEIT260344 cstr: 32379.14.JEIT260344

蒋伟进^{1, 3},
刘志华^{1, 3, ,},
崔新雨^{1, 3},
许宇胜²,
陈伸有^{1, 3},
胡佳龙^{1, 3}

1.
湖南工商大学计算机学院长沙 410205
2.
北方导航控制技术股份有限公司北京 100176
3.
湘江实验室长沙 410205

基金项目: 国家自然科学基金(61772196)，湖南省自然科学基金(2020JJ4249)，湖南省教育厅科学研究重点项目(24A0446, 24A0753)，湖南省研究生科研创新项目(CX20251694)

详细信息

作者简介:
蒋伟进：男，博士，二级教授，研究方向为边缘计算、联邦学习和网络空间安全

刘志华：男，研究生，研究方向为联邦学习和隐私保护

崔新雨：女，硕士生，研究方向为联邦学习和隐私保护

许宇胜：男，硕士，研究员级高级工程师，主要研究领域为联邦学习，网络空间安全和系统控制

陈伸有：男，硕士生，研究方向为联邦学习和隐私保护

胡佳龙：男，硕士生，研究方向为联邦学习和数据动态定价

通讯作者:
刘志华 212795753@qq.com

中图分类号: TP181
计量
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出版历程
- 收稿日期: 2026-03-24
- 修回日期: 2026-07-09
- 录用日期: 2026-07-09
- 网络出版日期: 2026-07-23

FedFACO: Personalized Federated Learning Method Based on Fisher Information Matrix for Adaptive Aggregation and Client Collaborative Optimization

JIANG Wei-Jin^{1, 3},
LIU Zhi-Hua^{1, 3
, ,},
CUI Xin-Yu^{1, 3},
XU Yu-Sheng²,
CHEN Shen-You^{1, 3},
HU Jia-Long^{1, 3}

1.
School of Computer Science, Hunan University of Technology and Business, Changsha, Hunan 410205, China
2.
Northern Navigation Control Technology Co., Ltd, Beijing 100176, China
3.
Xiangjiang Laboratory, Changsha 410205, China

Funds: The National Natural Science Foundation of China (61772196), Natural Science Foundation of Hunan Province (2020JJ4249), Key Scientific Research Project of Hunan Provincial Department of Education (24A0446, 24A0753), Hunan Provincial Graduate Student Research Innovation Project (CX20251694)

摘要

摘要: 联邦学习(FL)通过分布式协同训练保护数据隐私，但数据统计异构性、本地数据集动态更新及客户端参与异步性，导致现有方法在非独立同分布(Non-IID)场景下难以兼顾全局泛化与本地个性化需求。为此，本文提出了一种基于Fisher信息矩阵的自适应聚合与客户端协同优化的个性化联邦学习(FedFACO)方法，该方法通过自适应聚合(AA)机制与协同优化(CO)机制，增强了模型对异构数据的适应能力。首先，AA机制动态调整全局模型与本地模型的融合权重，有效缓解分布不匹配的问题并增强个性化能力；其次，CO机制执行双阶段协同优化，客户端采用参数对齐策略通过特征对齐与全局正则化约束实现全局知识与历史特征的平衡融合；服务器端采用基于Fisher信息矩阵(FIM)与数据量加权的复合客户端同步策略，有效抑制训练不足客户端的负面影响，提升了算法在极端异步环境和动态客户端场景下的适应性。实验结果表明，FedFACO在处理数据异构性时不仅可以显著提高模型在各客户端上的泛化性能，同时也保证了通信效率和模型鲁棒性。在多个非独立同分布数据集(MNIST、CIFAR-10/100、Tiny-ImageNet)上的实验表明，FedFACO相较于现有主流方法在准确率上提升了约3.1%，并在更具挑战性的Tiny-ImageNet数据集上，相较于最优基线，达到收敛所需的总训练时间降低了约4.8%。
- 联邦学习 /
- 数据异构性 /
- Fisher信息矩阵 /
- 自适应聚合 /
- 协同优化 /
- 个性化
Abstract: Objective Non-IID data heterogeneity remains one of the major challenges in personalized federated learning, as it often leads to inconsistent local optimization directions, insufficient global knowledge transfer, and degraded model personalization performance. To address these issues, this paper proposes FedFACO, a personalized federated learning method based on Fisher information matrix-guided adaptive aggregation and client collaborative optimization. The proposed method aims to improve the adaptability of federated models to heterogeneous client distributions while maintaining effective knowledge sharing across clients. By introducing an adaptive aggregation mechanism and a collaborative optimization strategy, FedFACO provides a more principled way to balance global generalization and local personalization, which is particularly important in complex Non-IID federated environments. Methods FedFACO consists of two key components. First, an adaptive aggregation (AA) mechanism is employed to dynamically adjust fusion weights between global and local models based on client-specific states, generating personalized initializations aligned with local data. Second, a collaborative optimization (CO) mechanism is introduced, combining feature alignment with FIM-based client weighting. This enhances useful global knowledge transfer and suppresses low-quality updates. The FIM is utilized to quantify the information contribution of each update, ensuring reliable aggregation. The method is evaluated on MNIST, CIFAR-10, CIFAR-100, and Tiny-ImageNet under Non-IID settings, and compared with representative baselines. Convergence behavior, dropout robustness, and sensitivity to low-quality updates are also examined. Results and Discussions Experimental results demonstrate that FedFACO consistently outperforms competitive baseline methods across all four benchmark datasets, achieving an average accuracy improvement of approximately 3.1% over mainstream approaches (Fig. 1, Table 2). On the more challenging Tiny-ImageNet dataset, FedFACO reduces the total training time required to reach convergence by approximately 4.8% compared with the best baseline (Table 3). Ablation studies confirm that performance is substantially improved by both AA and CO mechanisms, with their joint application yielding optimal accuracy (Table 6). Furthermore, FIM-guided weighting is shown to accurately quantify contribution quality in client dropout and asynchronous scenarios, significantly enhancing aggregation reliability (Fig. 2–Fig. 3). Superior robustness is also demonstrated in malicious client scenarios (Fig. 4). Conclusions This paper presents FedFACO, a personalized federated learning method for Non-IID environments via Fisher information matrix-guided adaptive aggregation and client collaborative optimization. The method effectively balances global knowledge sharing and local personalization while enhancing training stability and robustness under heterogeneous client participation. Experimental results validate its effectiveness and superiority in accuracy, convergence efficiency, and robustness. Future work will focus on lightweight Fisher information approximations and adaptive triggering strategies to reduce computational overhead, as well as integration with privacy-preserving and security-defense mechanisms for deployment in resource-constrained and high-security environments.
- Federated learning /
- Data heterogeneity /
- Fisher information matrix /
- Adaptive aggregation /
- Collaborative optimization /
- Personalization

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图 1 在$ \beta =0.1 $下,各方法在不同数据集上的测试准确率曲线

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图 2 对于CIFAR-100,各方法在不同狄利克雷参数$ \beta $和不同客户端在线比例$ P $的性能比较

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图 3 对于Tiny-ImageNet,各方法在不同狄利克雷参数$ \beta $和不同客户端在线比例$ P $的性能比较

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图 4 不同恶意客户端比例下各方法在三类数据集上的性能比较

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1 基于Fisher信息矩阵的自适应聚合与客户端协同优化的个性化联邦学习方法

输入：全局模型参数$ { \varTheta }^{0} $，客户端集合$ \left\{{C}_{1},{C}_{2},\cdots ,{C}_{N}\right\}， $每轮　参与训练的客户端在线比例$ P， $全局通信轮数$ T， $本地训练轮数　$ E， $客户端本地数据集$ {D}_{k}\left(k=1{,}2,\cdots ,N\right) $，高层聚合范围$ p $，　自适应权重矩阵$ {\boldsymbol{A}}_{k}， $本地模型$ {W}_{k}=\left({ \varTheta }_{k},{\omega }_{k}\right)， $本地学习率$ \eta $
输出：全局模型参数$ { \varTheta }^{T}， $各客户端个性化模型{$ W_{k}^{T} $}
1. 　服务器初始化全局模型参数$ { \varTheta }^{0}， $同步$ \varTheta _{k}^{0} \leftarrow { \varTheta }^{0} $
2. 　客户端将$ \boldsymbol{A}_{k}^{p}， \forall k\in \left[1{,}2,\cdots ,N\right]， $初始化为全1
3. 　FOR t = 1 TO T DO
4. 　　服务器从$ N $个客户端中随机选择$ \left\lceil P\cdot N\right\rceil $个客户端　　　　$ {S}_{k}\in\left\{{C}_{1},{C}_{2},\cdots ,{C}_{N}\right\} $
5. 　　//$ \text{客户端本地训练} $
6. 　　FOR ALL 客户端$ k\epsilon {S}_{k} $ DO
7. 　　　从服务器接收全局共享参数$ { \varTheta }^{t-1} $
8. 　　　读取上一轮训练后的本地共享参数$ \varTheta _{k}^{t-1} $和个性化头部　　　　　$ \omega _{k}^{t-1} $
9. 　　　// 自适应聚合(AA)
10. 　　 $ \Delta \leftarrow { \varTheta }^{t-1}{-\Theta}_{k}^{t-1} $
11. 　　 $ \tilde{ \varTheta }_{k}^{t}{=\Theta}_{k}^{t-1}+ \Delta \odot\left[{1}^{L-p};\sigma \left(\boldsymbol{A}_{k}^{p}\right)\right] $
12. 　　 $ \boldsymbol{A}_{k}^{p} \leftarrow \boldsymbol{A}_{k}^{p}-{\eta }_{AA}{\nabla}_{{\boldsymbol{A}_{k}^{p}}}{\text{L}}_{\text{task}}\left(\tilde{ \varTheta }_{k}^{t},{D}_{k},{ \varTheta }^{t-1}\right) $
13. 　　 // 协同优化—参数对齐(CO—PA)
14. 　　 $ E_{k}^{t-1}=f\left( \varTheta _{k}^{t-1},{D}_{k}\right),E_{k}^{t} $=$ f\left(\tilde{ \varTheta }_{k}^{t},{D}_{k}\right) $
15. 　　 $ \text{L}_{\text{align}}^{\text{feat}} \leftarrow \left\|\left\|E_{k}^{t}-E_{k}^{t-1}\right\|\right\|_{2}^{2} $
16. 　　 $ \text{L}_{\text{align}}^{\text{reg}} \leftarrow \left\|\left\|\tilde{ \varTheta }_{k}^{t}-{ \varTheta }^{t-1}\right\|\right\|_{2}^{2} $
17. 　　 $ {\mathcal{L}}_{\text{align}}\leftarrow \mathcal{L}_{\text{align}}^{\text{feat}}+\mathcal{L}_{\text{align}}^{\text{reg}} $
18. 　　 $ \varTheta _{k}^{t}=\tilde{ \varTheta }_{k}^{t}-\eta {\nabla}_{{\tilde{ \varTheta }_{k}^{t}}}{\text{L}}_{\text{align}}, \omega _{k}^{t}= \omega _{k}^{t-1} $
19. 　　 FOR e = 1 TO $ E $ DO
20. 　　　 $ {\text{L}}_{\text{task}} \leftarrow {\text{L}}_{\text{task}}\left({\varTheta }_{k}^{t}{, \omega }_{k}^{t};{D}_{k}\right) $
21. 　　　 $ \varTheta _{k}^{t}{ \leftarrow \varTheta }_{k}^{t}-\eta {\nabla}_{{ \varTheta _{k}^{t}}}{\text{L}}_{\text{task}} $
22. 　　　 $ \omega _{k}^{t}{ \leftarrow \omega }_{k}^{t}-\eta {\nabla}_{{ \omega _{k}^{t}}}{\text{L}}_{\text{task}} $
23. 　　 END FOR
24. 　　 // 协同优化—客户端同步(CO—CS)
25. 　　 $ {\boldsymbol{F}\boldsymbol{I}\boldsymbol{M}}_{\boldsymbol{k}} \leftarrow {\nabla}_{{{W}_{k}}}\ln p\left({D}_{k}\|{W}_{k}\right)\cdot{{{\nabla}_{{{W}_{k}}}}\ln p\left({D}_{k}\|{W}_{k}\right)}^{T} $
26. 　　 $ \overline{N}=\dfrac{1}{\left\| {S}_{k}\right\| }\displaystyle\sum\nolimits_{\text{j}\in{S}_{k}}{n}_{j} $
27. 　　 $ {\alpha }_{k} \leftarrow \displaystyle\sum\nolimits_{i=1}^{{d}_{w}}{\text{diag}\left({\text{FIM}}_{k}\right)}_{i}\cdot\ln \left(1+\dfrac{{n}_{k}}{\overline{N}}\right) $
28. 　　 $ \Delta {\varTheta }_{k}^{t}={\varTheta }_{k}^{t}-{{\varTheta }}^{t-1} $
29. 　　客户端上传$ \left\{ \Delta {\varTheta }_{k}^{t},{\alpha }_{k}\right\} $
30. 　 END FOR
31. 　 // 服务器聚合
32. 　 $ \alpha _{k}^{\prime}=\dfrac{{\alpha }_{k}}{\displaystyle\sum\limits_{\text{j}\in{S}_{k}}{\alpha }_{j}} $
33. 　 $ {{\varTheta }}^{t}={{\varTheta }}^{t-1}+\displaystyle\sum\nolimits_{k\in {S}_{k}}\alpha _{k}^{\prime} \Delta {\varTheta }_{k}^{t} $
34. END FOR
35. RETURN $ {{\varTheta }}^{T} $, {$ W_{k}^{T} $}

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表 1 联邦数据集统计信息

数据集	分类	类别数	样本数	分辨率
MNIST	Image	10	70,000	28x28
CIFAR-10	Image	10	60,000	32×32
CIFAR-100	Image	100	60,000	32×32
Tiny-ImageNet	Image	200	110,000	64×64

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表 2 不同数据集下,各方法不同狄利克雷参数$ \beta $的准确率比较

算法	MNIST			CIFAR-10			CIFAR-100			Tiny-ImageNet
算法	$ \beta $=0.1	$ \beta $=0.3	$ \beta $=0.5	$ \beta $=0.1	$ \beta $=0.3	$ \beta $=0.5	$ \beta $=0.1	$ \beta $=0.3	$ \beta $=0.5	$ \beta $=0.1	$ \beta $=0.3	$ \beta $=0.5
FedAvg	98.03	98.28	98.92	62.80	66.97	72.47	27.37	31.46	33.48	11.15	12.87	17.89
FedProx	98.12	98.47	98.96	63.21	67.49	72.58	32.18	34.80	36.74	12.21	15.81	17.96
FedALA	99.36	99.04	98.76	89.98	78.76	73.62	40.39	38.61	36.14	23.69	21.03	19.46
FedAS	99.49	99.12	99.06	90.16	81.45	77.01	44.16	41.25	41.15	23.78	22.48	21.48
pFedEC	99.39	99.02	98.92	89.83	79.57	73.60	45.68	34.12	32.87	20.55	19.38	18.57
FedAGHN	99.45	99.16	99.07	89.89	79.94	75.88	46.80	34.56	33.02	21.79	21.45	20.68
FedFACO	99.57	99.22	99.18	91.01	82.08	78.37	55.74	50.53	45.94	28.89	27.83	22.27

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表 3 不同方法的计算开销和通信开销

方法	总训练时间(h)	每轮平均时间(min)	通信开销
FedAvg	13.32	6.15	$ 2\cdot \sum $
FedProx	11.86	6.53	$ 2\cdot \sum $
FedALA	7.98	6.30	$ 2\cdot \sum $
FedAS	8.46	6.93	$ 2\cdot {\alpha }_{\mathrm{f}}\cdot \sum $
pFedEC	8.58	7.39	$ 2\cdot {\alpha }_{\mathrm{f}}\cdot \sum $
FedAGHN	9.17	8.18	$ 2\cdot \sum $
FedFACO	7.60	7.24	$ 2\cdot {\alpha }_{\mathrm{f}}\cdot \sum $

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表 4 不同在线比例下FIM对FedFACO收敛性能的影响

客户端在线比例	评估指标	FIM	w/o FIM	差异
$ P=0.2 $	准确率(%)	89.99	80.97	+9.02
$ P=0.2 $	收敛轮次	96	128	–32
$ P=0.6 $	准确率(%)	90.84	83.43	+7.41
$ P=0.6 $	收敛轮次	89	112	–23
$ P=1.0 $	准确率(%)	91.01	85.22	+5.79
$ P=1.0 $	收敛轮次	83	91	–8

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表 5 默认实际设置下CIFAR-100的PSNR($ \mathrm{dB},\downarrow $)值

方法	FedAvg	FedAS	pFedEC	FedAGHN	FedFACO
PSNR值	7.30	7.84	6.92	7.41	6.55

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表 6 FedFACO各模块在不同数据集上的准确率比较(%)

方法	AA模块	CO模块	MNIST	CIFAR- 10	CIFAR- 100	Tiny- ImageNet
Baseline (w/o AA&CO)	-	-	97.81	60.17	25.38	11.03
FedFACO w/o CO	√	-	98.61	81.74	38.41	20.56
FedFACO w/o AA	-	√	99.07	85.68	46.35	23.12
FedFACO	√	√	99.52	90.84	54.36	27.36

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