融合动态事件触发机制与差分隐私的在线分布式非凸优化

郑斌; 房肖

doi:10.16383/j.aas.c260311

融合动态事件触发机制与差分隐私的在线分布式非凸优化

doi: 10.16383/j.aas.c260311 cstr: 32138.14.j.aas.c260311

郑斌^1,,
房肖^2,

1.
东南大学数学学院南京 211189
2.
东南大学自动化学院南京 210096

基金项目: 国家重点研发计划项目(2022YFA1004702), 国家自然科学基金(U22B2046), 江苏省基础研究计划(BK20253020)资助

详细信息

作者简介:
郑斌：东南大学数学学院博士研究生. 主要研究方向为多智能体系统分布式优化. E-mail: zhengqiaomu88@163.com

房肖：东南大学自动化学院博士后. 主要研究方向为多智能体系统分布式优化与博弈论. 本文通信作者. E-mail: fangxiao@seu.edu.cn

计量
- 文章访问数: 15
- HTML全文浏览量: 9
- 被引次数: 0
出版历程
- 收稿日期: 2026-05-12
- 录用日期: 2026-06-24
- 网络出版日期: 2026-10-14

Online Distributed Nonconvex Optimization Integrating Dynamic Event-Triggered Mechanism and Differential Privacy

ZHENG Bin^1
,,
FANG Xiao^2
,

1.
School of Mathematics, Southeast University, Nanjing 211189
2.
School of Automation, Southeast University, Nanjing 210096

Funds: Supported by National Key Research and Development Program of China (2022YFA1004702), National Natural Science Foundation of China (U22B2046), and Basic Research Program of Jiangsu (BK20253020)

More Information

Author Bio:
ZHENG Bin　Ph.D. candidate at the School of Mathematics, Southeast University, Nanjing, China. His main research interest is distributed optimization

FANG Xiao　Postdoctoral fellow at School of Automation, Southeast University, Nanjing, China. Her research interest covers distributed optimization and game theory. Corresponding author of this paper

摘要

摘要: 研究通信资源受限下非平衡有向多智能体网络的分布式在线优化隐私保护问题. 针对智能体初始状态及局部目标函数的隐私需求, 通过引入Laplace噪声实现差分隐私保护, 并设计含控制因子的动态事件触发机制以降低通信开销. 在此基础上, 构建了一套适用于非凸函数的事件触发与差分隐私分布式优化算法, 有效防止敏感信息泄露. 理论分析证明了算法在非平衡有向网络中的收敛性能及其隐私保护水平. 仿真结果验证动态事件触发机制与差分隐私协同下算法的可行性与有效性.
- 在线分布式优化 /
- 差分隐私 /
- 动态事件触发 /
- 非凸函数 /
- 不平衡网络
Abstract: This paper investigates the problem of privacy preservation in distributed online optimization over unbalanced directed multi-agent networks under communication resource constraints. To protect the privacy of agents' initial states and local cost functions, Laplace noise is introduced to achieve differential privacy, and a dynamic event-triggered mechanism with a control factor is designed to reduce communication overhead. Based on this, an event-triggered differential privacy distributed optimization algorithm for non-convex functions is developed, which effectively prevents sensitive information leakage. Theoretical analysis proves the convergence of the proposed algorithm in unbalanced directed networks and characterizes its achieved privacy protection level. Simulation results validate the feasibility and effectiveness of the algorithm under the synergy of the dynamic event-triggered mechanism and differential privacy.
- Distributed online optimization /
- differentially private /
- dynamic event-triggering /
- nonconvex function /
- unbalanced network

HTML全文

图 1 每个智能体的梯度遗憾

Fig. 1 Per-agent gradient regret

下载: 全尺寸图片幻灯片

图 2 不同控制因子下算法1的梯度遗憾

Fig. 2 Gradient regret of Algorithm 1 for different control factors

下载: 全尺寸图片幻灯片

图 3 不同算法的比较

Fig. 3 Comparison of different algorithms

下载: 全尺寸图片幻灯片

表 1 动态事件触发参数

Table 1 Dynamic event-triggered parameters

智能体	$\gamma_i$	$\omega_i$	$\varsigma_i$	$\phi_i$
1	0.96	0.80	2.00	0.50
2	0.96	0.80	3.00	0.50
3	0.96	0.90	2.00	0.50
4	0.96	0.80	2.00	0.60
5	0.96	0.90	2.00	0.50
6	0.96	0.90	2.00	0.20

下载: 导出CSV

表 2 动态事件触发次数

Table 2 Dynamic event-triggered count

智能体	触发次数	总更新次数
1	261	300
2	260	300
3	271	300
4	257	300
5	267	300
6	289	300

下载: 导出CSV

表 3 算法1不同控制因子比较

Table 3 Comparison of Algorithm 1 for different control factors

因子	$ [1,\;100)$	$ [100,\;200)$	$ [200,\;300]$
$\nu_1$	1	1	1
$\nu_2$	1.2	1	0.9
$\nu_3$	1.5	1	0.7
$\nu_4$	2	1	0.5

下载: 导出CSV

表 4 不同控制因子下智能体的触发次数

Table 4 Agent trigger counts under different control factors

智能体	$\nu_1$	$\nu_2$	$\nu_3$	$\nu_4$
1	209	205	205	208
2	211	207	203	198
3	213	209	208	202
4	201	194	173	162
5	212	213	209	209
6	243	245	234	230

下载: 导出CSV

表 5 不同算法比较

Table 5 Comparison of different algorithms

触发机制	总触发次数	平均触发次数
没有触发	1800	300
静态触发^[40]	1675	279
动态触发	1572	262

下载: 导出CSV

参考文献(46)

[1]	Steven R, Klymenko O V, Short M. Machine learning-accelerated distributed optimisation methods for optimal power flow-a review. Renewable and Sustainable Energy Reviews, 2026, 226: Article No. 116190 doi: 10.1016/j.rser.2025.116190
[2]	Al-Tawaha A, Cibaku E, Park S, Lavaei J, Jin M. Distributed optimization and distributed learning: A paradigm shift for power systems. IEEE Systems Journal, 2025, 19(4): 1038−1051 doi: 10.1109/JSYST.2025.3602318
[3]	Wen G H, Zheng W X, Wan Y. Distributed robust optimization for networked agent systems with unknown nonlinearities. IEEE Transactions on Automatic Control, 2023, 68(9): 5230−5244 doi: 10.1109/TAC.2022.3216965
[4]	Butler E, Xie Y, Lin Z. Distributed multileader formation tracking within a weight-unbalanced directed network of multiple agents. IEEE Transactions on Control of Network Systems, 2025, 12(4): 2798−2810 doi: 10.1109/TCNS.2025.3590502
[5]	Han D, Deng W, Zhao Z, Pei W, Xiao H. Coordinated optimization of active distribution network and multi-microgrids considering voltage robustness and economic efficiency: A distributed model predictive control method. IET Generation, Transmission & Distribution, 2025, 19(1): Article No. e70130 doi: 10.1049/gtd2.70130
[6]	Shi S, Miyata S, Akashi Y. A hybrid multi-agent distributed optimal control strategy of multizone VAV systems for edge computing in smart buildings. Energy and Buildings, 2025, 345: Article No. 116089 doi: 10.1016/j.enbuild.2025.116089
[7]	Tsitsiklis J, Bertsekas D, Athans M. Distributed asynchronous deterministic and stochastic gradient optimization algorithms. IEEE Transactions on Automatic Control, 1986, 31(9): 803−812 doi: 10.1109/TAC.1986.1104412
[8]	Bertsekas D P, Tsitsiklis J N. Parallel and Distributed Computation: Numerical Methods. Englewood Cliffs: Prentice Hall, 1989.
[9]	崔秋燕, 纪志坚. 分布式优化研究进展. 控制理论与应用, 2025, 42(11): 2196−2206 doi: 10.7641/CTA.2025.50100 Cui Qiu-Yan, Ji Zhi-Jian. Advances in distributed optimization. Control Theory & Applications, 2025, 42(11): 2196−2206 doi: 10.7641/CTA.2025.50100
[10]	Liu S, Hua Y, Han Q L, Xie L. Distributed optimization under information constraints: A survey. IEEE Transactions on Industrial Informatics, 2026, 22(4): 2653−2666 doi: 10.1109/TII.2025.3645932
[11]	Sun C, Zhang H, Chen B, Yu L. Distributed stochastic optimization under heavy-tailed noises. IEEE Transactions on Automatic Control, 2026, 71(3): 1885−1892 doi: 10.1109/TAC.2025.3617572
[12]	Qin Y, Lu K, Xu H, Chen X. High probability convergence of clipped distributed dual averaging with heavy-tailed noises. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2025, 55(4): 2624−2632 doi: 10.1109/TSMC.2024.3525011
[13]	Yu Z, Ho D W C, Yuan D, Shi Z. Distributed composite optimization with distributed composite block mirror descent. IEEE Transactions on Automatic Control, 2026, 71(6): 4081−4088 doi: 10.1109/TAC.2026.3652901
[14]	Jiang X, Zeng X, Xie L, Sun J, Chen J. Distributed stochastic projection-free algorithm for constrained optimization. IEEE Transactions on Automatic Control, 2025, 70(4): 2479−2494 doi: 10.1109/TAC.2024.3481040
[15]	Luan M, Wen G H, Lv Y Z, Zhou J L, Chen C L P. Distributed constrained optimization over unbalanced time-varying digraphs: A randomized constraint solving algorithm. IEEE Transactions on Automatic Control, 2024, 69(8): 5154−5167 doi: 10.1109/TAC.2023.3347328
[16]	Zinkevich M. Online convex programming and generalized infinitesimal gradient ascent. In: Proceedings of the 20th International Conference on Machine Learning (ICML). Washington, USA: AAAI Press, 2003. 928-936
[17]	Hazan E. Introduction to online convex optimization. Foundations and Trends in Optimization, 2016, 2(3-4): 157−325 doi: 10.1561/2400000013
[18]	Hazan E, Agarwal A, Kale S. Logarithmic regret algorithms for online convex optimization. Machine Learning, 2007, 69(2-3): 169−192 doi: 10.1007/s10994-007-5016-8
[19]	Hazan E, Singh K, Zhang C. Efficient regret minimization in non-convex games. In: Proceedings of the 34th International Conference on Machine Learning (ICML). Sydney, Australia: PMLR, 2017. 1433-1441
[20]	Li J Y, Li C J, Fan J, Huang T W. Online distributed stochastic gradient algorithm for nonconvex optimization with compressed communication. IEEE Transactions on Automatic Control, 2024, 69(2): 936−951 doi: 10.1109/TAC.2023.3327183
[21]	Liao L, Yuan D, Ho D W C, Zheng W X, Zhang B, Yu Z. Distributed dynamic no-regret learning in two-network zero-sum games. IEEE Transactions on Automatic Control, 2026, 71(1): 183−197 doi: 10.1109/TAC.2025.3586980
[22]	Lu K H, Jing G S, Wang L. Online distributed optimization with strongly pseudoconvex-sum cost functions. IEEE Transactions on Automatic Control, 2020, 65(1): 426−433 doi: 10.1109/TAC.2019.2915745
[23]	Lagendijk R L, Erkin Z, Barni M. Encrypted signal processing for privacy protection: Conveying the utility of homomorphic encryption and multiparty computation. IEEE Signal Processing Magazine, 2013, 30(1): 82−105 doi: 10.1109/MSP.2012.2219653
[24]	Wan Y, Cao J D, Chen G R, Huang W. Distributed observer-based cyber-security control of complex dynamical networks. IEEE Transactions on Circuits and Systems I: Regular Papers, 2017, 64(11): 2966−2975 doi: 10.1109/TCSI.2017.2708113
[25]	Mo Y, Murray R M. Privacy preserving average consensus. IEEE Transactions on Automatic Control, 2017, 62(2): 753−765 doi: 10.1109/TAC.2016.2564339
[26]	Benhamouda F, Halevi S, Halevi T. Supporting private data on hyperledger fabric with secure multiparty computation. IBM Journal of Research and Development, 2019, 63(2/3): 1−8
[27]	Huang Z Q, Mitra S, Vaidya N. Differentially private distributed optimization. In: Proceedings of the 16th International Conference on Distributed Computing and Networking (ICDCN). Goa, India: ACM Press, 2015.
[28]	Nozari E, Tallapragada P, Cortés J. Differentially private distributed convex optimization via functional perturbation. IEEE Transactions on Control of Network Systems, 2017, 5(1): 395−408
[29]	Zhu J L, Xu C Q, Guan J F, Wu D O. Differentially private distributed online algorithms over time-varying directed networks. IEEE Transactions on Signal and Information Processing over Networks, 2018, 4(1): 4−17 doi: 10.1109/TSIPN.2018.2797806
[30]	Ding T, Zhu S Y, He J P, Guan X P. Differentially private distributed optimization via state and direction perturbation in multiagent systems. IEEE Transactions on Automatic Control, 2022, 67(2): 722−737 doi: 10.1109/TAC.2021.3059427
[31]	Wang Y Q, Nedić A. Tailoring gradient methods for differentially private distributed optimization. IEEE Transactions on Automatic Control, 2024, 69(2): 872−887 doi: 10.1109/TAC.2023.3272968
[32]	Wang Y, Başar T. Decentralized nonconvex optimization with guaranteed privacy and accuracy. Automatica, 2023, 150: Article No. 110858 doi: 10.1016/j.automatica.2023.110858
[33]	Chen J L, Wang J M, Zhang J F. Differentially private distributed nonconvex stochastic optimization with quantized communication. IEEE Transactions on Automatic Control, 2026, 71(1): 368−383 doi: 10.1109/TAC.2025.3590872
[34]	Peng C, Li F. A survey on recent advances in event-triggered communication and control. Information Sciences, 2018, 457: 113−125
[35]	Chen W, Ren W. Event-triggered zero-gradient-sum distributed consensus optimization over directed networks. Automatica, 2016, 65: 90−97 doi: 10.1016/j.automatica.2015.11.015
[36]	Liu J Y, Chen W S, Dai H. Event-triggered zero-gradient-sum distributed convex optimisation over networks with time-varying topologies. International Journal of Control, 2019, 92(12): 2829−2841 doi: 10.1080/00207179.2018.1460693
[37]	杨涛, 徐磊, 易新蕾, 张圣军, 陈蕊娟, 李渝哲. 基于事件触发的分布式优化算法. 自动化学报, 2022, 48(1): 133−143 doi: 10.16383/j.aas.c200838 Yang Tao, Xu Lei, Yi Xin-Lei, Zhang Sheng-Jun, Chen Rui-Juan, Li Yu-Zhe. Event-triggered distributed optimization algorithms. Acta Automatica Sinica, 2022, 48(1): 133−143 doi: 10.16383/j.aas.c200838
[38]	Liu C X, Li H P, Shi Y, Xu D M. Distributed event-triggered gradient method for constrained convex minimization. IEEE Transactions on Automatic Control, 2020, 65(2): 778−785 doi: 10.1109/TAC.2019.2916985
[39]	Li H Q, Liu S, Soh Y C, Xie L H. Event-triggered communication and data rate constraint for distributed optimization of multiagent systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018, 48(11): 1908−1919 doi: 10.1109/TSMC.2017.2694323
[40]	Mao S, Yang M L, Yang W, Tang Y, Zheng W X, Gu J P, et al. Differentially private distributed optimization with an event-triggered mechanism. IEEE Transactions on Circuits and Systems I: Regular Papers, 2023, 70(7): 2943−2956 doi: 10.1109/TCSI.2023.3266358
[41]	Xiong M H, Yang C Y, Zhao J G, Zhang B Y, Yuan D M. Static and dynamic regrets for online distributed composite optimization: Edge-based dynamic event-triggered algorithms. IEEE Transactions on Automatic Control, 2026, 71(5): 2887−2902 doi: 10.1109/TAC.2025.3632693
[42]	熊梦辉, 杨春雨, 赵建国, 张保勇, 袁德明. 基于边缘动态事件触发的在线分布式复合Bandit优化算法. 自动化学报, 2025, 51(8): 1811−1828 doi: 10.16383/j.aas.c250070 Xiong Meng-Hui, Yang Chun-Yu, Zhao Jian-Guo, Zhang Bao-Yong, Yuan De-Ming. Edge dynamic event-triggered-based online distributed composite Bandit optimization algorithm. Acta Automatica Sinica, 2025, 51(8): 1811−1828 doi: 10.16383/j.aas.c250070
[43]	He W L, Luo T H, Tang Y, Du W L, Tian Y C, Qian F. Secure communication based on quantized synchronization of chaotic neural networks under an event-triggered strategy. IEEE Transactions on Neural Networks and Learning Systems, 2020, 31(9): 3334−3345 doi: 10.1109/TNNLS.2019.2943548
[44]	Zhang Z, Lun Z J, Sun Y, Lu Z. Dynamic event-triggered communication based distributed optimization. International Journal of Robust and Nonlinear Control, 2021, 31(17): 8504−8522 doi: 10.1002/rnc.5732
[45]	Yuan Y, He W L, Du W L, Tian Y C, Han Q L, Qian F. Distributed gradient tracking for differentially private multi-agent optimization with a dynamic event-triggered mechanism. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2024, 54(5): 3044−3055 doi: 10.1109/TSMC.2024.3357253
[46]	Mai V S, Abed E H. Distributed optimization over directed graphs with row stochasticity and constraint regularity. Automatica, 2019, 102: 94−104 doi: 10.1016/j.automatica.2018.07.020