Geodesic
Distributed aggregative optimization with quantized communication
Kybernetika, Tome 58 (2022) no. 1, pp. 123-144
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In this paper, we focus on an aggregative optimization problem under the communication bottleneck. The aggregative optimization is to minimize the sum of local cost functions. Each cost function depends on not only local state variables but also the sum of functions of global state variables. The goal is to solve the aggregative optimization problem through distributed computation and local efficient communication over a network of agents without a central coordinator. Using the variable tracking method to seek the global state variables and the quantization scheme to reduce the communication cost spent in the optimization process, we develop a novel distributed quantized algorithm, called D-QAGT, to track the optimal variables with finite bits communication. Although quantization may lose transmitting information, our algorithm can still achieve the exact optimal solution with linear convergence rate. Simulation experiments on an optimal placement problem is carried out to verify the correctness of the theoretical results.
In this paper, we focus on an aggregative optimization problem under the communication bottleneck. The aggregative optimization is to minimize the sum of local cost functions. Each cost function depends on not only local state variables but also the sum of functions of global state variables. The goal is to solve the aggregative optimization problem through distributed computation and local efficient communication over a network of agents without a central coordinator. Using the variable tracking method to seek the global state variables and the quantization scheme to reduce the communication cost spent in the optimization process, we develop a novel distributed quantized algorithm, called D-QAGT, to track the optimal variables with finite bits communication. Although quantization may lose transmitting information, our algorithm can still achieve the exact optimal solution with linear convergence rate. Simulation experiments on an optimal placement problem is carried out to verify the correctness of the theoretical results.
DOI : 10.14736/kyb-2022-1-0123
Classification : 68W15, 90C33
Keywords: distributed aggregative optimization; multi-agent network; quantized communication; linear convergence rate 
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Chen, Ziqin; Liang, Shu. Distributed aggregative optimization with quantized communication. Kybernetika, Tome 58 (2022) no. 1, pp. 123-144. doi: 10.14736/kyb-2022-1-0123

[1] Barbarossa, S., Sardellitti, S., Lorenzo, P. D.: Communicating while computing: Distributed mobile cloud computing over 5G heterogeneous networks. IEEE Signal Process. Mag. 31 (2014), 45-55. | DOI

[2] Cao, X., Liu, K. J. R.: Distributed Newton's method for network cost minimization. IEEE Trans. Automat. Control 66 (2021), 1278-1285. | DOI | MR

[3] Cheng, S., Liang, S.: Distributed optimization for multi-agent system over unbalanced graphs with linear convergence rate. Kybernetika 56 (2020), 559-577. | DOI | MR

[4] Chen, J., Sayed, A.: Diffusion adaptation strategies for distributed optimization and learning over networks. IEEE Trans. Signal Process. 60 (2012), 4289-4305. | DOI | MR

[5] Deng, Z., Liang, S.: Distributed algorithms for aggregative games of multiple heterogeneous Euler-Lagrange systems. Automatica 99 (2019), 246-252. | DOI | MR

[6] Persis, C. De, Grammatico, S.: Continuous-time integral dynamics for a class of aggregative games with coupling constraints. IEEE Trans. Automat. Control 65 (2020), 2171-2176. | DOI | MR

[7] Horn, R. A., Johnson, C. R: Matrix Analysis. Cambridge University Press, New York 2012. | MR | Zbl

[8] Jakovetic, D., Moura, J. M. F., Xavier, J.: Linear convergence rate of a class of distributed augmented Lagrangian algorithms. IEEE Trans. Automat. Control 60 (2015), 922-936. | DOI | MR

[9] Kajiyama, Y., Hayashi, N., Takai, S.: Linear convergence of consensus-based quantized optimization for smooth and strongly convex cost functions. IEEE Trans. Automat. Control 66 (2020), 1254-1261. | DOI | MR

[10] Lan, G., Lee, S., Zhou, Y.: Communication-efficient algorithms for decentralized and stochastic optimization. Math. Program. 180 (2020), 237-284. | DOI | MR

[11] Li, P., Hu, J.: A solution strategy for distributed uncertain economic dispatch problems via scenario theory. Control Theory Technol. 19 (2021), 499-506. | DOI | MR

[12] Li, P., Hu, J., Qiu, L., Zhao, Y., Ghosh, B.: A distributed economic dispatch strategy for power-water networks. IEEE Trans. Control Netw. Syst., Early Access (2021). | DOI

[13] Li, X., Xie, L., Hong, Y.: Distributed continuous-time algorithm for a general nonsmooth monotropic optimization problem. Int. J. Robust Nonlinear Control 29 (2019), 3252-3266. | DOI | MR

[14] Li, X., Xie, L., Hong, Y.: Distributed aggregative optimization over multi-agent networks. IEEE Trans. Automat. Control. Early Access (2021). | DOI

[15] Ma, J., Yu, X., Liu, L., Feng, G.: Global cooperative output regulation of linear multi-agent systems with limited bandwidth. IEEE Trans. Control Netw. Syst., Early Access (2021). | DOI

[16] Magnussson, S., Shokri-Ghadikolaei, H., Li, N.: On maintaining linear convergence of distributed learning and optimization under limited communication. IEEE Trans. Signal Process. 68 (2020), 6101-6116. | DOI | MR

[17] Msechu, E. J., Giannakis, G. B.: Sensor-centric data reduction for estimation with WSNs via censoring and quantization. IEEE Trans. Signal Process. 60 (2011), 400-414. | DOI | MR

[18] Nedic, A.: Distributed gradient methods for convex machine learning problems in networks: Distributed optimization. IEEE Signal Process. Mag. 73 (2020), 92-101. | DOI

[19] Nedic, A., Ozdaglar, A.: Distributed subgradient methods for multi-agent optimization. IEEE Trans. Autom. Control 54 (2009), 48-61. | DOI | MR

[20] Pu, Y., Zeilinger, M. N., Jones, C. N.: Quantization design for distributed optimization. IEEE Trans. Automat. Control 62 (2016), 2107-2120. | DOI | MR

[21] Ren, W., Beard, R. W.: Distributed consensus in multi-vehicle cooperative control. Springer, London 2008.

[22] Shi, W., Ling, Q., Wu, G., Yin, W.: EXTRA: An exact first-order algorithm for decentralized consensus optimization. SIAM J. Optim. 25 (2015), 944-966. | DOI | MR

[23] Tardos, E., Vazirani, V. V.: Basic solution concepts and computational issues. Algorithmic Game Theory (2007), 3-28. | DOI | MR

[24] Wang, X., Deng, Z., Ma, S., Xian, D.: Event-triggered design for multi-agent optimal consensus of Euler-Lagrangian systems. Kybernetika 53 (2017), 179-194. | DOI | MR

[25] Wang, Y., Lin, P., Qin, H.: Distributed classification learning based on nonlinear vector support machines for switching networks. Kybernetika 53 (2017), 595-611. | DOI | MR

[26] Xu, J., Zhu, S., Soh, Y. C., Xie, L.: A Bregman splitting scheme for distributed optimization over networks. IEEE Trans. Automat. Control 63 (2018), 3809-3824. | DOI | MR

[27] Yi, P., Hong, Y.: Quantized subgradient algorithm and data-rate analysis for distributed optimization. IEEE Trans. Control Netw. Syst. 1 (2014), 380-392. | DOI | MR

[28] Yi, P., Hong, Y., Liu, F.: Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and its application to economic dispatch of power systems. Automatica 74 (2016), 259-269. | DOI | MR

[29] Yuan, D., Hong, Y., Ho, D., Jiang, G.: Optimal distributed stochastic mirror descent for strongly convex optimization. Automatica 90 (2018), 196-203. | DOI | MR

[30] Zhang, X., Liu, J., Zhu, Z., Bentley, E. S.: Compressed distributed gradient descent: Communication-efficient consensus over networks. In: Proc. IEEE Conf. Comput. Commun. 2019, 2431-2439. | DOI

[31] Zhu, S., Hong, M., Chen, B.: Quantized consensus ADMM for multi-agent distributed optimization. In: Proc. IEEE Int. Conf. Acoust., Speech Signal Process 2016, pp. 4134-4138. | DOI

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