Quality-aware incentive mechanism based on Stackelberg game for federated learning in internet of vehicles

doi:10.11772/j.issn.1001-9081.2025060784

Abstract

Abstract:

Focusing on the issues of Non-Independent and Identically Distributed （Non-IID） data， low-quality data contributed by vehicle participants， and insufficient incentives in Internet of Vehicles （IoV）' Federated Learning （FL）， a quality-aware incentive mechanism based on Stackelberg game for federated learning in IoV was proposed. First， a clustering method based on the similarity of gradient optimization directions of vehicle participants was designed to reduce the impact of Non-IID data on model convergence and improve training efficiency. Second， a dual-dimensional quality evaluation metric was developed that combined gradient direction consistency and loss reduction to measure data quality， and a joint incentive was implemented according to data contribution. Furthermore， a Stackelberg game model was constructed to describe the interaction among cloud servers， edge servers， and vehicle clients， and the optimal strategy combination was derived using backward induction， with the existence and uniqueness of the Stackelberg equilibrium analyzed. Simulation results show that the proposed quality-aware incentive mechanism outperforms baseline mechanisms， achieving significant improvements in both social utility and cloud server utility. Compared with FedAS （Federated parameter-Alignment and client-Synchronization）， the proposed mechanism improves the accuracy by 0.28%， 1.77%， and 5.08% on the MNIST， CIFAR-10， and BelgiumTSC datasets， respectively， verifying the superiority and effectiveness of this mechanism.

Key words: Internet of Vehicles (IoV), Federated Learning (FL), incentive mechanism, quality-aware, Stackelberg game

摘要：

针对车联网联邦学习（FL）中的非独立同分布（Non-IID）数据、车辆参与者贡献低质量数据和激励不足等问题，提出一种车联网中基于Stackelberg博弈的联邦学习质量感知激励机制。首先，设计一种基于车辆参与者梯度优化方向相似性的聚类方法，以减轻Non-IID数据对模型收敛的影响，提高训练效率；其次，提出双维度质量评价指标，结合梯度方向一致性和损失下降幅度衡量数据质量，并根据数据贡献量进行联合激励；进一步地，采用Stackelberg博弈模型描述云服务器、边缘服务器以及车辆客户端之间的交互过程，使用逆向归纳法求解最优策略组合，深入探讨了Stackelberg均衡的存在性和唯一性。仿真实验结果表明，本文提出的质量感知激励机制优于基线机制，其社会效用和云服务器效用均显著提升；与FedAS （Federated parameter-Alignment and client-Synchronization）相比，该机制在MNIST、CIFAR-10和BelgiumTSC数据集上的准确率分别提升了0.28%、1.77%和5.08%，验证了其优势和有效性。

关键词: 车联网, 联邦学习, 激励机制, 质量感知, Stackelberg博弈

CLC Number:

TP393.0

Tianle SUN, Tengfei CAO. Quality-aware incentive mechanism based on Stackelberg game for federated learning in internet of vehicles[J]. Journal of Computer Applications, 2026, 46(7): 2229-2238.

孙天乐, 曹腾飞. 车联网中基于Stackelberg博弈的联邦学习质量感知激励机制[J]. 《计算机应用》唯一官方网站, 2026, 46(7): 2229-2238.

Figures/Tables 6

Fig. 1 Framework of hierarchical federated learning system for internet of vehicles

Tab. 1 Simulation parameters setting

参数	值	说明
$I$	100	客户端总数
$ζ$	5	边缘服务器数量
$τ$	6	本地训练轮数
$W$	10 MHz	通信带宽
$c i$	50 cycle/bit	车辆 $i$ 处理单个比特所需的CPU周期数
$f i$	10 GHz	车辆 $i$ 的CPU计算能力
$p i$	0.5 W	客户端发射功率
$λ$	25	云服务器效用系统参数
$β n$	1	边缘服务器奖励缩放系数

Tab. 1 Simulation parameters setting

参数	值	说明
$I$	100	客户端总数
$ζ$	5	边缘服务器数量
$τ$	6	本地训练轮数
$W$	10 MHz	通信带宽
$c i$	50 cycle/bit	车辆 $i$ 处理单个比特所需的CPU周期数
$f i$	10 GHz	车辆 $i$ 的CPU计算能力
$p i$	0.5 W	客户端发射功率
$λ$	25	云服务器效用系统参数
$β n$	1	边缘服务器奖励缩放系数

Fig. 2 Comparison of multiple mechanisms of social utility and cloud server utility under varying numbers of clients and edge servers without low-quality data

Fig. 3 Comparison of multiple mechanisms of social utility and cloud server utility under varying numbers of clients and edge servers with 30% low-quality data

Fig. 4 Cloud server utility under different weight mechanisms

Fig. 5 Comparison of model test accuracy on different datasets

References 32

[1]	刘淼，林婉茹，王琴，等.车联网联邦学习的数据异质性问题及基于个性化的解决方法综述［J］.通信学报， 2024， 45（10）： 207-224.
	Liu Miao， Lin Wanru， Wang Qin， et al. Survey on data heterogeneity problems and personalization based solutions of federated learning in Internet of vehicles ［J］. Journal on Communications， 2024， 45（10）： 207-224.
[2]	Yin L， Luo J， Qiu C， et al. Joint task offloading and resources allocation for hybrid vehicle edge computing systems ［J］. IEEE Transactions on Intelligent Transportation Systems， 2024， 25（8）： 10355-10368.
[3]	Kumar A S， Zhao L， Fernando X. Asynchronous federated based vehicular edge computation offloading ［J］. IEEE Transactions on Vehicular Technology， 2024， 73（12）： 19350-19360.
[4]	巫婕，钱雪忠，宋威.基于相似度聚类和正则化的个性化联邦学习［J］.计算机应用， 2024， 44（11）： 3345-3353.
	Wu Jie， Qian Xuezhong， Song Wei. Personalized federated learning based on similarity clustering and regularization ［J］. Journal of Computer Applications， 2024， 44（11）： 3345-3353.
[5]	唐晓岚，梁煜婷，陈文龙.面向非独立同分布数据的车联网多阶段联邦学习机制［J］.计算机研究与发展， 2024， 61（9）： 2170-2184.
	Tang Xiaolan， Liang Yuting， Chen Wenlong. Multi-stage federated learning mechanism with non-IID data in internet of vehicles ［J］. Journal of Computer Research and Development， 2024， 61（9）： 2170-2184.
[6]	You C， Guo K， Yang H H， et al. Hierarchical personalized federated learning over massive mobile edge computing networks ［J］. IEEE Transactions on Wireless Communications， 2023， 22（11）： 8141-8157.
[7]	McMahan H B， Moore E， Ramage D， et al. Communication-efficient learning of deep networks from decentralized data ［C］// AISTATS 2017. New York： JMLR.org， 2017： 1273-1282.
[8]	Liu L， Zhang J， Song S H， et al. Client-edge-cloud hierarchical federated learning ［C］// ICC 2020. Piscataway： IEEE， 2020： 1-6.
[9]	Arisdakessian S， Wahab O A， Mourad A， et al. Coalitional federated learning： improving communication and training on non-IID data with selfish clients ［J］. IEEE Transactions on Services Computing， 2023， 16（4）： 2462-2476.
[10]	Liao G， Luo B， Feng Y， et al. Optimal mechanism design for heterogeneous client sampling in federated learning ［J］. IEEE Transactions on Mobile Computing， 2024， 23（11）： 10598-10609.
[11]	Pan Z， Li Y， Guan Z， et al. RFCSC： communication efficient reinforcement federated learning with dynamic client selection and adaptive gradient compression ［J］. Neurocomputing， 2025， 612： No.128672.
[12]	Wang P， Song W， Qi H， et al. Server-initiated federated unlearning to eliminate impacts of low-quality data ［J］. IEEE Transactions on Services Computing， 2024， 17（3）： 1196-1211.
[13]	Wang D， Ren J， Wang Z， et al. PrivAim： a dual-privacy preserving and quality-aware incentive mechanism for federated learning ［J］. IEEE Transactions on Computers， 2023， 72（7）： 1913-1927.
[14]	Wu A， Yu J， Wang Y， et al. Prototype-decomposed knowledge distillation for learning generalized federated representation ［J］. IEEE Transactions on Multimedia， 2024， 26： 10991-11002.
[15]	Zhao Z， Wang J， Hong W， et al. Ensemble federated learning with non-IID data in wireless networks ［J］. IEEE Transactions on Wireless Communications， 2024， 23（4）： 3557-3571.
[16]	Qi J， Lin F， Chen Z， et al. High-quality model aggregation for blockchain-based federated learning via reputation-motivated task participation ［J］. IEEE Internet of Things Journal， 2022， 9（19）： 18378-18391.
[17]	Wang S， Zhao H， Wen W， et al. Contract theory based incentive mechanism for clustered vehicular federated learning ［J］. IEEE Transactions on Intelligent Transportation Systems， 2024， 25（7）： 8134-8147.
[18]	Yao Y， Li G， Chen H， et al. Incentive mechanism design for semi-asynchronous federated learning based on contract theory： a learning approach ［J］. IEEE Internet of Things Journal， 2025， 12（15）： 30901-30920.
[19]	Li Y， Yang B， Wu H， et al. Joint offloading decision and resource allocation for vehicular fog-edge computing networks： a contract-Stackelberg approach ［J］. IEEE Internet of Things Journal， 2022， 9（17）： 15969-15982.
[20]	Kim T， Kim J， Lee H， et al. An efficient winner and payment determination algorithm in reverse auction for edge federation ［J］. IEEE Transactions on Network and Service Management， 2025， 22（2）： 1945-1954.
[21]	Li J， Chen Z， Zang T， et al. Reinforcement learning-based dual-identity double auction in personalized federated learning ［J］. IEEE Transactions on Mobile Computing， 2025， 24（5）： 4086-4103.
[22]	Li G， Cai J， Lu J， et al. Incentive mechanism design for cross-device federated learning： a reinforcement auction approach ［J］. IEEE Transactions on Mobile Computing， 2025， 24（4）： 3059-3075.
[23]	Cheng S， Ren T， Zhang H， et al. A Stackelberg game based framework for edge pricing and resource allocation in mobile edge computing ［J］. IEEE Internet of Things Journal， 2024， 11（11）： 20514-20530.
[24]	He W， Yao H， Mai T， et al. Three-stage Stackelberg game enabled clustered federated learning in heterogeneous UAV swarms ［J］. IEEE Transactions on Vehicular Technology， 2023， 72（7）： 9366-9380.
[25]	Xu Y， Xiao M， Wu J， et al. Incentive mechanism for spatial crowdsourcing with unknown social-aware workers： a three-stage Stackelberg game approach ［J］. IEEE Transactions on Mobile Computing， 2023， 22（8）： 4698-4713.
[26]	Hu C L， Lin K Y， Chang C K. Incentive mechanism for mobile crowdsensing with two-stage Stackelberg game ［J］. IEEE Transactions on Services Computing， 2023， 16（3）： 1904-1918.
[27]	Xu Q， Su Z， Li P， et al. Cooperative energy provisioning services with virtual power plants in smart grid internet of things： a coalition-Stackelberg game approach ［J］. IEEE Internet of Things Journal， 2025， 12（16）： 32980-32993.
[28]	Zeng B， Yang X， Chen Y， et al. Federated data quality assessment approach： robust learning with mixed label noise ［J］. IEEE Transactions on Neural Networks and Learning Systems， 2024， 35（12）： 17620-17634.
[29]	Yang Y， Wang W， Liu L， et al. AoI optimization in the UAV-aided traffic monitoring network under attack： a Stackelberg game viewpoint ［J］. IEEE Transactions on Intelligent Transportation Systems， 2023， 24（1）： 932-941.
[30]	Tian S， Xiang S， Zhou Z， et al. Task offloading and resource allocation based on reinforcement learning and load balancing in vehicular networking ［J］. IEEE Transactions on Consumer Electronics， 2025， 71（1）： 2217-2230.
[31]	Zhan Y， Li P， Qu Z， et al. A learning-based incentive mechanism for federated learning ［J］. IEEE Internet of Things Journal， 2020， 7（7）： 6360-6368.
[32]	Yang X， Huang W， Ye M. FedAS： bridging inconsistency in personalized federated learning ［C］// ICCV 2024. Piscataway： IEEE， 2024： 11986-11995.