Privacy Distributed Constrained Optimization Over Time-Varying Unbalanced Networks and Its Application in Federated Learning

Mengli Wei; Wenwu Yu; Duxin Chen; Mingyu Kang; Guang Cheng

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 15.3, Top 1 (SCI Q1)

CiteScore: 23.5, Top 2% (Q1)
Google Scholar h5-index: 77， TOP 5

Article Contents

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2025 > In Press, Accepted Manuscript

M. Wei, W. Yu, D. Chen, M. Kang, and G. Cheng, “Privacy distributed constrained optimization over time-varying unbalanced networks and its application in federated learning,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 2, pp. 1–12, Feb. 2025.

Citation:

M. Wei, W. Yu, D. Chen, M. Kang, and G. Cheng, “Privacy distributed constrained optimization over time-varying unbalanced networks and its application in federated learning,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 2, pp. 1–12, Feb. 2025.

Citation:

M. Wei, W. Yu, D. Chen, M. Kang, and G. Cheng, “Privacy distributed constrained optimization over time-varying unbalanced networks and its application in federated learning,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 2, pp. 1–12, Feb. 2025.

PDF( 2537 KB)

Privacy Distributed Constrained Optimization Over Time-Varying Unbalanced Networks and Its Application in Federated Learning

Funds: This work was supported in part by the National Key Research and Development Program of China (2022ZD0120001), the National Natural Science Foundation of China (62233004, 62273090, 62073076), and the Jiangsu Provincial Scientific Research Center of Applied Mathematics (BK20233002)

More Information

Author Bio:
Mengli Wei received the B.S. degree in automation and the M.S. degree in control science and engineering from Chongqing University. He is currently a Ph.D. degree candidate in Southeast University. His research interests include decentralized federated learning, distributed optimization and cyberspace security for complex networks and systems science

Wenwu Yu (Senior Member, IEEE) received the B.Sc. degree in information and computing science and the M.Sc. degree in applied mathematics from the Department of Mathematics, Southeast University, in 2004 and 2007, respectively, and the Ph.D. degree from the Department of Electronic Engineering, City University of Hong Kong, China in 2010. Currently, he is the Dean in the School of Mathematics, the Deputy Associate Director of National Center of Applied Mathematics, Southeast University of Jiangsu, the Deputy Director of Jiangsu Provincial Scientific Research Center of Applied Mathematics, Deputy Associate Director of Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, and a Full Professor with the Endowed Chair Honor in Southeast University. He held several visiting positions in Australia, China, Germany, Italy, the Netherlands, and the USA. His research interests include multi-agent systems, complex networks and systems, disturbance control, distributed optimization, machine learning, game theory, cyberspace security, smart grids, intelligent transportation systems, big-data analysis, etc. Dr. Yu severs as an Editorial Board Member of several flag journals, including IEEE Transactions on Circuits and Systems II, IEEE Trans. Industrial Cyber-Physical Systems, IEEE Transactions on Industrial Informatics, IEEE Transactions on Systems, Man, and Cybernetics: Systems, Science China Information Sciences, Science China Technological Sciences, etc. He was listed by Clarivate Analytics/Thomson Reuters Highly Cited Researchers in Engineering in 2014-2023. He publishes about 100 IEEE Transactions journal papers with more than 20 000 citations. Moreover, he is also the recipient of the Second Prize of State Natural Science Award of China in 2016. He is also the Cheung Kong Scholars Programmer of Ministry of Education of China (Artificial Intelligence)

Duxin Chen (Member, IEEE) received the B.S. degree in automatic control and the Ph.D. degree in control science and engineering from the Huazhong University of Science and Technology, in 2013 and 2018, respectively. He is currently an Associate Professor with the School of Mathematics, and Vice Director of the Jiangsu Provincial Scientific Research Center of Applied Mathematics, Southeast University. He is also one of the Direction Leaders of the Huawei-SEU Joint Innovation Laboratory of Networked Collective Intelligence. His research interests include causal inference, prediction/generation, and system identification techniques for complex networks and systems science, artificial intelligence related theory and applications

Mingyu Kang received the M.S. degree in computer technology from Southeast University in 2021. He is currently a Ph.D candidate with the Jiangsu Key Laboratory of Networked Collective Intelligence, the School of Cyber Science and Engineering, Southeast University. His research interests include complex system, complex network, deep learning and causal inference

Guang Cheng (Member, IEEE) received the B. S. degree in traffic engineering from Southeast University in 1994, the M. S. degree in computer application from Hefei University of Technology in 2000, and the Ph. D. degree in computer network from Southeast University in 2003. He is currently a Full Professor with the School of Cyber Science and Engineering, Southeast University. He has authored or coauthored eight monographs and produced more than100technical papers, including top journals and top conferences, such as IEEE/ACM Transactions on Networking, IEEE Transactions on Information Forensics and Security, IEEE Transactions on Industrial Informatics, and INFOCOM. His research interests include network security, network measurement, and traffic analysis. He is the Director of Jiangsu Cyber Security Association, China; and the Vice Director of China Computer Federation Technical Committee of Internet(CCF TCI) and Jiangsu Computer Society, China. He is a Distinguished Member of CCF
Corresponding author: Wenwu Yu, e-mail: wwyu@seu.edu.cn
Received Date: 2023-11-30
Revised Date: 2024-07-21
Accepted Date: 2024-08-15

Available Online: 2024-11-15

Abstract

Abstract

This paper investigates a class of constrained distributed zeroth-order optimization (ZOO) problems over time-varying unbalanced graphs while ensuring privacy preservation among individual agents. Not taking into account recent progress and addressing these concerns separately, there remains a lack of solutions offering theoretical guarantees for both privacy protection and constrained ZOO over time-varying unbalanced graphs. We hereby propose a novel algorithm, termed the differential privacy (DP) distributed push-sum based zeroth-order constrained optimization algorithm (DP-ZOCOA). Operating over time-varying unbalanced graphs, DP-ZOCOA obviates the need for supplemental suboptimization problem computations, thereby reducing overhead in comparison to distributed primary-dual methods. DP-ZOCOA is specifically tailored to tackle constrained ZOO problems over time-varying unbalanced graphs, offering a guarantee of convergence to the optimal solution while robustly preserving privacy. Moreover, we provide rigorous proofs of convergence and privacy for DP-ZOCOA, underscoring its efficacy in attaining optimal convergence without constraints. To enhance its applicability, we incorporate DP-ZOCOA into the federated learning framework and formulate a decentralized zeroth-order constrained federated learning algorithm (ZOCOA-FL) to address challenges stemming from the time-varying imbalance of communication topology. Finally, the performance and effectiveness of the proposed algorithms are thoroughly evaluated through simulations on distributed least squares (DLS) and decentralized federated learning (DFL) tasks.

FullText(HTML)

References(49)

References

[1]	J. Verbraeken, M. Wolting, J. Katzy, J. Kloppenburg, T. Verbelen, and J. S. Rellermeyer, “A survey on distributed machine learning,” ACM Computing Surveys (csur), vol. 53, no. 2, pp. 1–33, 2020.
[2]	J. Liu, J. Huang, Y. Zhou, X. Li, S. Ji, H. Xiong, and D. Dou, “From distributed machine learning to federated learning: A survey,” Knowledge and Information Systems, vol. 64, no. 4, pp. 885–917, 2022. doi: 10.1007/s10115-022-01664-x
[3]	X. Wang, Y. Han, C. Wang, Q. Zhao, X. Chen, and M. Chen, “In-edge ai: Intelligentizing mobile edge computing, caching and communication by federated learning,” IEEE Network, vol. 33, no. 5, pp. 156–165, 2019. doi: 10.1109/MNET.2019.1800286
[4]	T. Yang, X. Yi, J. Wu, Y. Yuan, D. Wu, Z. Meng, Y. Hong, H. Wang, Z. Lin, and K. H. Johansson, “A survey of distributed optimization,” Annu. Reviews in Control, vol. 47, pp. 278–305, 2019. doi: 10.1016/j.arcontrol.2019.05.006
[5]	A. Nedić and A. Olshevsky, “Distributed optimization over time-varying directed graphs,” IEEE Trans. Autom. Control, vol. 60, no. 3, pp. 601–615, 2015. doi: 10.1109/TAC.2014.2364096
[6]	A. Nedic, A. Olshevsky, and W. Shi, “Achieving geometric convergence for distributed optimization over time-varying graphs,” SIAM J. Optimization, vol. 27, no. 4, pp. 2597–2633, 2017. doi: 10.1137/16M1084316
[7]	A. Nedic, A. Olshevsky, W. Shi, and C. A. Uribe, “Geometrically convergent distributed optimization with uncoordinated step-sizes,” in Proc. American Control Conf., 2017, pp. 3950–3955.
[8]	S. Liang and G. Yin, “Dual averaging push for distributed convex optimization over time-varying directed graph,” IEEE Trans. Autom. Control, vol. 65, no. 4, pp. 1785–1791, 2019.
[9]	C. Wang, S. Xu, D. Yuan, Y. Chu, and Z. Zhang, “Cooperative convex optimization with subgradient delays using push-sum distributed dual averaging,” J. Franklin Institute, vol. 358, no. 14, pp. 7254–7269, 2021. doi: 10.1016/j.jfranklin.2021.07.015
[10]	G. Scutari and Y. Sun, “Distributed nonconvex constrained optimization over time-varying digraphs,” Mathematical Programming, vol. 176, pp. 497–544, 2019. doi: 10.1007/s10107-018-01357-w
[11]	J. Li, C. Gu, Z. Wu, and T. Huang, “Online learning algorithm for distributed convex optimization with time-varying coupled constraints and bandit feedback,” IEEE Trans. Cybern., vol. 52, no. 2, pp. 1009–1020, 2020.
[12]	X. Li, X. Yi, and L. Xie, “Distributed online optimization for multi-agent networks with coupled inequality constraints,” IEEE Trans. Autom. Control, vol. 66, no. 8, pp. 3575–3591, 2020.
[13]	Z. He, J. He, C. Chen, and X. Guan, “Constrained distributed nonconvex optimization over time-varying directed graphs,” in Proc. 59th IEEE Conf. Decision and Control , 2020, pp. 378–383.
[14]	Q. Lü, H. Li, Z. Wang, Q. Han, and W. Ge, “Performing linear convergence for distributed constrained optimisation over time-varying directed unbalanced networks,” IET Control Theory & Applications, vol. 13, no. 17, pp. 2800–2810, 2019.
[15]	S. Lee, A. Nedić, and M. Raginsky, “Stochastic dual averaging for decentralized online optimization on time-varying communication graphs,” IEEE Trans. Autom. Control, vol. 62, no. 12, pp. 6407–6414, 2017. doi: 10.1109/TAC.2017.2650563
[16]	C. Wang and S. Xu, “Distributed online constrained optimization with feedback delays,” IEEE Trans. Neural Networks and Learning Systems, pp. 1–13, 2022.
[17]	D. Wang, J. Liu, J. Lian, Y. Liu, Z. Wang, and W. Wang, “Distributed delayed dual averaging for distributed optimization over time-varying digraphs,” Automatica, vol. 150, p. 110869, 2023. doi: 10.1016/j.automatica.2023.110869
[18]	W. Yu, H. Liu, W. X. Zheng, and Y. Zhu, “Distributed discrete-time convex optimization with nonidentical local constraints over time-varying unbalanced directed graphs,” Automatica, vol. 134, p. 109899, 2021. doi: 10.1016/j.automatica.2021.109899
[19]	J. Zimmermann, T. Tatarenko, V. Willert, and J. Adamy, “Projected push-sum gradient descent-ascent for convex optimization with application to economic dispatch problems,” in Proc. 59th IEEE Conf. Decision and Control, 2020, pp. 542–547.
[20]	C. Dwork and A. Roth, “The algorithmic foundations of differential privacy,” Foundations and Trends® in Theoretical Computer Science, vol. 9, no. 3-4, pp. 211–407, 2014.
[21]	Y. Xiong, X. Li, K. You, and L. Wu, “Distributed online optimization in time-varying unbalanced networks without explicit subgradients,” IEEE Trans. Signal Processing, vol. 70, pp. 4047–4060, 2022. doi: 10.1109/TSP.2022.3194369
[22]	C. Gu, L. Jiang, J. Li, and Z. Wu, “Privacy-preserving dual stochastic push-sum algorithm for distributed constrained optimization,” J. Optimization Theory and Applications, pp. 1–29, 2023.
[23]	Q. Lü, X. Liao, T. Xiang, H. Li, and T. Huang, “Privacy masking stochastic subgradient-push algorithm for distributed online optimization,” IEEE Trans. Cybernetics, vol. 51, no. 6, pp. 3224–3237, 2020.
[24]	S. Mao, Y. Tang, Z. Dong, K. Meng, Z. Y. Dong, and F. Qian, “A privacy preserving distributed optimization algorithm for economic dispatch over time-varying directed networks,” IEEE Trans. Industrial Informatics, vol. 17, no. 3, pp. 1689–1701, 2021. doi: 10.1109/TII.2020.2996198
[25]	Q. Xu, C. Yu, X. Yuan, Z. Fu, and H. Liu, “A privacy-preserving distributed subgradient algorithm for the economic dispatch problem in smart grid,” IEEE/CAA J. Autom. Sinica, 2022.
[26]	D. Han, K. Liu, Y. Lin, and Y. Xia, “Differentially private distributed online learning over time-varying digraphs via dual averaging,” Int. J. Robust and Nonlinear Control, vol. 32, no. 5, pp. 2485–2499, 2022. doi: 10.1002/rnc.5635
[27]	K. Zhang, X. Liao, and Q. Lü, “Privacy-protected decentralized dual averaging push with edge-based correlated perturbations over time-varying directed networks,” IEEE Trans. Network Science and Engineering, vol. 9, no. 6, pp. 4145–4158, 2022. doi: 10.1109/TNSE.2022.3195953
[28]	M. Wei, J. Yang, Z. Zhao, X. Zhang, J. Li, and Z. Deng, “Defedhdp: Fully decentralized online federated learning for heart disease prediction in computational health systems,” IEEE Trans. Computational Social Systems, pp. 1–14, 2024.
[29]	T. Li, A. K. Sahu, A. Talwalkar, and V. Smith, “Federated learning: Challenges, methods, and future directions,” IEEE Signal Processing Magazine, vol. 37, no. 3, pp. 50–60, 2020. doi: 10.1109/MSP.2020.2975749
[30]	J. Zhao, H. Zhu, F. Wang, R. Lu, Z. Liu, and H. Li, “PVD-FL: A privacy-preserving and verifiable decentralized federated learning framework,” IEEE Trans. Infor. Forensics and Security, vol. 17, pp. 2059–2073, 2022. doi: 10.1109/TIFS.2022.3176191
[31]	Q. Chen, Z. Wang, H. Wang, and X. Lin, “Feddual: Pair-wise gossip helps federated learning in large decentralized networks,” IEEE Trans. Inform. Forensics and Security, vol. 18, pp. 335–350, 2023. doi: 10.1109/TIFS.2022.3222935
[32]	Q. Yang, Y. Liu, T. Chen, and Y. Tong, “Federated machine learning: Concept and applications,” ACM Trans. Intelligent Systems and Technology, vol. 10, no. 2, pp. 1–19, 2019.
[33]	Y. Yuan, J. Liu, D. Jin, et al., “DECEFL: A principled decentralized federated learning framework,” arXiv preprint arXiv: 2107.07171, 2021.
[34]	Y. Lu, Z. Yu, and N. Suri, “Privacy-preserving decentralized federated learning over time-varying communication graph,” arXiv preprint arXiv: 2210.00325, 2022.
[35]	S. Savazzi, M. Nicoli, and V. Rampa, “Federated learning with cooperating devices: A consensus approach for massive iot networks,” IEEE Internet of Things J., vol. 7, no. 5, pp. 4641–4654, 2020. doi: 10.1109/JIOT.2020.2964162
[36]	Y. Lu, X. Huang, K. Zhang, S. Maharjan, and Y. Zhang, “Blockchain empowered asynchronous federated learning for secure data sharing in internet of vehicles,” IEEE Trans. Vehicular Technology, vol. 69, no. 4, pp. 4298–4311, 2020. doi: 10.1109/TVT.2020.2973651
[37]	X. Yi, X. Li, T. Yang, L. Xie, T. Chai, and K. H. Johansson, “Distributed bandit online convex optimization with time-varying coupled inequality constraints,” IEEE Trans. Autom. Control, vol. 66, no. 10, pp. 4620–4635, 2021. doi: 10.1109/TAC.2020.3030883
[38]	D. Yuan, B. Zhang, D. W. Ho, W. X. Zheng, and S. Xu, “Distributed online bandit optimization under random quantization,” Automatica, vol. 146, p. 110590, 2022. doi: 10.1016/j.automatica.2022.110590
[39]	C. Wang, S. Xu, D. Yuan, D. Yuan, B. Zhang, and Z. Zhang, “Push-sum distributed online optimization with bandit feedback,” IEEE Trans. Cybern., pp. 1–11, 2020.
[40]	W. Fang, Z. Yu, Y. Jiang, Y. Shi, C. N. Jones, and Y. Zhou, “Communication-efficient stochastic zeroth-order optimization for federated learning,” IEEE Trans. Signal Processing, vol. 70, pp. 5058–5073, 2022. doi: 10.1109/TSP.2022.3214122
[41]	Z. Li and L. Chen, “Communication-efficient decentralized zeroth-order method on heterogeneous data,” in Proc. IEEE 13th Int. Conf. Wireless Communi. and Signal Processing, 2021, pp. 1–6.
[42]	L. Deng, “The mnist database of handwritten digit images for machine learning research[best of the web],” IEEE Signal Proc. Magazine, vol. 29, no. 6, pp. 141–142, 2012. doi: 10.1109/MSP.2012.2211477
[43]	S. Liu, P.-Y. Chen, B. Kailkhura, G. Zhang, A. O. Hero III, and P. K. Varshney, “A primer on zeroth-order optimization in signal processing and machine learning: Principals, recent advances, and applications,” IEEE Signal Proc. Magazine, vol. 37, no. 5, pp. 43–54, 2020. doi: 10.1109/MSP.2020.3003837
[44]	G. Hinton, “The forward-forward algorithm: Some preliminary investigations,” arXiv preprint arXiv: 2212.13345, 2022.
[45]	A. Nedic, A. Ozdaglar, and P. A. Parrilo, “Constrained consensus and optimization in multi-agent networks,” IEEE Trans. Autom. Control, vol. 55, no. 4, pp. 922–938, 2010. doi: 10.1109/TAC.2010.2041686
[46]	H. Liu, W. X. Zheng, and W. Yu, “Distributed discrete-time algorithms for convex optimization with general local constraints on weight-unbalanced digraph,” IEEE Trans. Control of Network Systems, vol. 8, no. 1, pp. 51–64, 2020.
[47]	M. J. Islam, S. Ahmad, F. Haque, M. B. I. Reaz, M. A. S. Bhuiyan, and M. R. Islam, “Application of min-max normalization on subject-invariant emg pattern recognition,” IEEE Trans. Instrumentation and Measurement, vol. 71, pp. 1–12, 2022.
[48]	B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y Arcas, “Communication-efficient learning of deep networks from decentralized data,” in Proc. Artificial Intelligence and Statistics, 2017, pp. 1273–1282.
[49]	S. Warnat-Herresthal, H. Schultze, K. L. Shastry, et al., “Swarm learning for decentralized and confidential clinical machine learning,” Nature, vol. 594, no. 7862, pp. 265–270, 2021. doi: 10.1038/s41586-021-03583-3

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(5) / Tables(1)

Get Citation

PDF

XML

Article Metrics

Article views (101) PDF downloads(37)

Privacy Distributed Constrained Optimization Over Time-Varying Unbalanced Networks and Its Application in Federated Learning

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Export File

Citation

Format

Content