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Logarithmic Communication for Distributed Optimization in Multi-Agent Systems

Published: 17 December 2019 Publication History

Abstract

Classically, the design of multi-agent systems is approached using techniques from distributed optimization such as dual descent and consensus algorithms. Such algorithms depend on convergence to global consensus before any individual agent can determine its local action. This leads to challenges with respect to communication overhead and robustness, and improving algorithms with respect to these measures has been a focus of the community for decades.
This paper presents a new approach for multi-agent system design based on ideas from the emerging field of local computation algorithms. The framework we develop, LOcal Convex Optimization (LOCO), is the first local computation algorithm for convex optimization problems and can be applied in a wide-variety of settings. We demonstrate the generality of the framework via applications to Network Utility Maximization (NUM) and the distributed training of Support Vector Machines (SVMs), providing numerical results illustrating the improvement compared to classical distributed optimization approaches in each case.

References

[1]
Dimitris Achlioptas, Themis Gouleakis, and Fotis Iliopoulos. 2018. Local Computation Algorithms for the Lová sz Local Lemma. CoRR, Vol. abs/1809.07910 (2018). http://arxiv.org/abs/1809.07910
[2]
Amr Ahmed, Mohamed Aly, Joseph Gonzalez, Shravan Narayanamurthy, and Alexander Smola. 2012. Scalable inference in latent variable models. In Proc. of the 5th ACM WSDM. 123--132.
[3]
Noga Alon, Ronitt Rubinfeld, Shai Vardi, and Ning Xie. 2012. Space-Efficient Local Computation Algorithms. In Proc. 22ndACM-SIAM Symposium on Discrete Algorithms (SODA). 1132--1139.
[4]
Ganesh Ananthanarayanan, Michael Chien-Chun Hung, Xiaoqi Ren, Ion Stoica, Adam Wierman, and Minlan Yu. 2014. GRASS: Trimming Stragglers in Approximation Analytics. In 11th USENIX Symposium on Networked Systems Design and Implementation (NSDI 14).
[5]
Reid Andersen, ChristianBorgs, Jennifer Chayes, John Hopcraft, Vahab S. Mirrokni, and Shang-Hua Teng. 2008. Local Computation of PageRank Contributions. Internet Mathematics, Vol. 5(1--2) (2008), 23--45.
[6]
Yossi Azar, Niv Buchbinder, T-H. Hubert Chan, Shahar Chen, Ilan Reuven Cohen, Anupam Gupta, Zhiyi Huang, Ning Kang, Viswanath Nagarajan, Joseph (Seffi) Naor, and Debmalya Panigrahi. 2016. Online algorithms for covering and packing problems with convex objectives. In Proc. of the IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS). 148--157.
[7]
Amrit Singh Bedi and Ketan Rajawat. 2017. Asynchronous Incremental Stochastic Dual Descent Algorithm for Network Resource Allocation. IEEE Transactions on Signal Processing, Vol. 66 (2017), 2229--2244.
[8]
Jacobus F. Benders. 1962. Partitioning procedures for solving mixed-variables programming problems. Numer. Math., Vol. 4, 1 (1962), 238--252.
[9]
Dimitri P. Bertsekas. 1999. Nonlinear programming .Athena Scientific.
[10]
Dimitri P. Bertsekas and John N. Tsitsiklis. 1989. Parallel and Distributed Computation: Numerical Methods .Prentice Hall.
[11]
Vincent D. Blondel, Julien M. Hendrickx, Alex Olshevsky, and John N. Tsitsiklis. 2005. Convergence in multiagent coordination, consensus, and flocking. In Proc. of IEEE Conference on Decision and Control. 2996--3000.
[12]
Sem Borst, Varun Gupta, and Anwar Walid. 2010. Distributed caching algorithms for content distribution networks. In Proceedings of IEEE INFOCOM. 1--9.
[13]
Stephen Boyd, Neal Parikh, Eric Chu, Borja Peleato, and Jonathan Eckstein. 2011. Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. and Trends in Machine Learning, Vol. 3, 1 (2011), 1--122.
[14]
Niv Buchbinder and Joseph (Seffi) Naor. 2009. The Design of Competitive Online Algorithms via a Primal-Dual Approach. Foundations and Trends in Theoretical Computer Science, Vol. 3, 2--3 (2009), 93--263.
[15]
CAIDA. 2007., Vol. The CAIDA UCSD AS Relationship Dataset http://www.caida.org/data/as-relationships/ (2007).
[16]
Tsung-Hui Chang, Mingyi Hong, Wei-Cheng Liao, and Xiangfeng Wang. 2016. Asynchronous Distributed ADMM for Large-Scale Optimization-Part I: Algorithm and Convergence Analysis. IEEE Transactions on Signal Processing, Vol. 64, 12 (2016), 3118--3130.
[17]
Nikolaos Chatzipanagiotis, Darinka Dentcheva, and Michael M. Zavlanos. 2015. An Augmented Lagrangian Method for Distributed Optimization. Math. Program., Vol. 152, 1--2 (2015), 405--434.
[18]
Yudong Chen, Lili Su, and Jiaming Xu. 2017. Distributed Statistical Machine Learning in Adversarial Settings: Byzantine Gradient Descent. Proc. ACM Meas. Anal. Comput. Syst. SIGMETRICS, Vol. 1, 2 (2017).
[19]
Mung Chiang, Steven H Low, A Robert Calderbank, and John C Doyle. 2007. Layering as optimization decomposition: A mathematical theory of network architectures. Proc. IEEE, Vol. 95, 1 (2007), 255--312.
[20]
Patrick L. Combettes and Valerie R. Wajs. 2005. Signal recovery by proximal forward-backward splitting. Multiscale Modeling & Simulation, Vol. 4, 4 (2005), 1168--1200.
[21]
Corinna Cortes and Vladimir Vapnik. 1995. Support-vector networks. Machine Learning, Vol. 20, 3 (1995), 273--297.
[22]
George Dantzig. 2016. Linear programming and extensions .Princeton university press.
[23]
George B. Dantzig and Philip Wolfe. 1960. Decomposition principle for linear programs. Oper. Res., Vol. 8, 1 (1960), 101--111.
[24]
Reza Eghbali and Maryam Fazel. 2016. Designing smoothing functions for improved worst-case competitive ratio in online optimization. In Neural Information Processing Systems. 3287--3295.
[25]
Tomaso Erseghe. 2014. Distributed optimal power flow using ADMM. IEEE Trans. on Power Sys., Vol. 29, 5 (2014), 2370--2380.
[26]
Tomaso Erseghe, Davide Zennaro, Emiliano Dall'Anese, and Lorenzo Vangelista. 2011. Fast Consensus by the Alternating Direction Multipliers Method. IEEE Trans. on Sig. Proces., Vol. 59 (2011), 5523--5537.
[27]
Uriel Feige, Boaz Patt-Shamir, and Shai Vardi. 2018. On the Probe Complexity of Local Computation Algorithms. In 45th International Colloquium on Automata, Languages, and Programming, (ICALP). 50:1--50:14.
[28]
Pedro A Forero, Alfonso Cano, and Georgios B. Giannakis. 2010. Consensus-Based Distributed Support Vector Machines. J. Mach. Learn. Res., Vol. 11 (2010), 1663--1707.
[29]
Daniel Gabay and Bertrand Mercier. 1976. A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications, Vol. 2, 1 (1976), 17--40.
[30]
Lingwen Gan, Ufuk Topcu, and Steven H. Low. 2013. Optimal decentralized protocol for electric vehicle charging. IEEE Transactions on Power Systems, Vol. 28, 2 (2013), 940--951.
[31]
Tom Goldstein, Gavin Taylor, Kawika Barabin, and Kent Sayre. 2016. Unwrapping ADMM: Efficient Distributed Computing via Transpose Reduction. In AISTATS. 1151--1158.
[32]
Joseph E. Gonzalez, Yucheng Low, Carlos E. Guestrin, and David O'Hallaron. 2009. Distributed parallel inference on large factor graphs. In Proc. of the 25th Conf. on UIAI. 203--212.
[33]
Carlos Guestrin, Peter Bodik, Romain Thibaux, Mark Paskin, and Samuel Madden. 2004. Distributed regression: an efficient framework for modeling sensor network data. In Proceedings of the 3rd ACM IPSN. 1--10.
[34]
Yi Guo and Lynne E Parker. 2002. A distributed and optimal motion planning approach for multiple mobile robots. In Robotics and Automation, 2002. Proceedings. ICRA'02. IEEE International Conference on, Vol. 3. 2612--2619.
[35]
Tamir Hazan, Amit Man, and Amnon Shashua. 2008. A parallel decomposition solver for SVM: Distributed dual ascend using fenchel duality. In Proc. of CVPR. 1--8.
[36]
Jianghai Hu, Yingying Xiao, and Ji Liu. 2018. Distributed Algorithms for Solving Locally Coupled Optimization Problems on Agent Networks. In Decision and Control (CDC), 2007 IEEE Annual Conference on. IEEE, 2420--2425.
[37]
Hugh Everett III. 1963. Generalized Lagrange multiplier method for solving problems of optimum allocation of resources. Operations research, Vol. 11, 3 (1963), 399--417.
[38]
Thorsten Joachims. 2006. Training Linear SVMs in Linear Time. In Proceedings of the 12th ACM SIGKDD. 217--226.
[39]
Jonathan Katz and Luca Trevisan. 2000. On the efficiency of local decoding procedures for error-correcting codes. In Proc. 32nd Annual ACM Symposium on the Theory of Computing (STOC). 80--86.
[40]
Frank P. Kelly, A. K. Maulloo, and David K. H. Tan. 1998. Rate control for communication networks: shadow prices, proportional fairness and stability. J. of the Operational Research Society, Vol. 49, 3 (1998), 237--252.
[41]
Sarit Khirirat, Mikael Johansson, and Dan Alistarh. 2018. Gradient compression for communication-limited convex optimization. In 2018 IEEE Conference on Decision and Control (CDC). 166--171.
[42]
Jakub Konecný, H. Brendan McMahan, and Daniel Ramage. 2015. Federated Optimization: Distributed Optimization Beyond the Datacenter. ArXiv, Vol. abs/1511.03575 (2015).
[43]
Christos Koufogiannakis and Neal E. Young. 2011. Distributed algorithms for covering, packing and maximum weighted matching. Distributed Computing, Vol. 24, 1 (2011), 45--63.
[44]
Yoshiaki Kuwata and Jonathan P How. 2011. Cooperative distributed robust trajectory optimization using receding horizon MILP. IEEE Transactions on Control Systems Technology, Vol. 19, 2 (2011), 423--431.
[45]
Leon S Lasdon. 1970. Optimization theory for large systems .Courier Corporation.
[46]
Reut Levi and Ronitt Rubinfeld andAnak Yodpinyanee. 2015. Brief Announcement: Local Computation Algorithms for Graphs of Non-Constant Degrees. In Proc. of the 27th ACM on Symposium on Parallelism in Algorithms and Architectures, (SPAA). 59--61.
[47]
David D. Lewis, Yiming Yang, Tony G. Rose, and Fan Li. 2004. RCV1: A New Benchmark Collection for Text Categorization Research. Journal of Machine Learning Research., Vol. 5 (2004), 361--397.
[48]
Na Li, Lijun Chen, and Steven H Low. 2011. Optimal demand response based on utility maximization in power networks. In IEEE Power and Energy Society General Meeting. 1--8.
[49]
Ying Liao, Huan Qi, and Weiqun Li. 2013. Load-balanced clustering algorithm with distributed self-organization for wireless sensor networks. IEEE Sensors Journal, Vol. 13, 5 (2013), 1498--1506.
[50]
Steven H. Low and David E. Lapsley. 1999. Optimization flow control. I. Basic algorithm and convergence. IEEE/ACM Transactions on Networking, Vol. 7, 6 (1999), 861--874.
[51]
Steven H Low, Fernando Paganini, and John C Doyle. 2002. Internet congestion control. IEEE Control Systems, Vol. 22, 1 (2002), 28--43.
[52]
Sindri Magnússon, Chinwendu Enyioha, Na Li, Carlo Fischione, and Vahid Tarokh. 2018a. Communication Complexity of Dual Decomposition Methods for Distributed Resource Allocation Optimization. IEEE Journal of Selected Topics in Signal Processing, Vol. 12, 4 (2018), 717--732.
[53]
Sindri Magnússon, Chinwendu Enyioha, Na Li, Carlo Fischione, and Vahid Tarokh. 2018b. Convergence of limited communication gradient methods. IEEE Journal of Selected Topics in Signal Processing, Vol. 63, 5 (2018), 1356--1371.
[54]
Yishay Mansour, Aviad Rubinstein, Shai Vardi, and Ning Xie. 2012. Converting Online Algorithms to Local Computation Algorithms. In Proc. of 39th Intl. Colloq. on Automata, Lang. and Prog. (ICALP). 653--664.
[55]
Laurent Massoulié and James Roberts. 1999. Bandwidth sharing: objectives and algorithms. In IEEE INFOCOM, Vol. 3. 1395--1403.
[56]
Brendan McMahan and Daniel Ramage. Accessed: 2017-04--10. Federated learning: Collaborative machine learning without centralized training data. https:// research.googleblog.com/ 2017/ 04/ federated-l earning-collaborative.html.
[57]
Damon Mosk-Aoyama, Tim Roughgarden, and Devavrat Shah. 2010. Fully distributed algorithms for convex optimization problems. SIAM J. on Opt., Vol. 20, 6 (2010), 3260--3279.
[58]
Jo ao F. C. Mota, Jo ao M. F. Xavier, Pedro M. Q. Aguiar, and Markus Püschel. 2013. D-ADMM: A communication-efficient distributed algorithm for separable optimization. IEEE Trans. on Sig. Proces., Vol. 61, 10 (2013), 2718--2723.
[59]
Angelia Nedic and Asuman Ozdaglar. 2007. On the Rate of Convergence of Distributed Subgradient Methods for Multi-agent Optimization. In Decision and Control (CDC), 2007 IEEE 46th Annual Conference on. IEEE, 4711--4716.
[60]
Angelia Nedic and Asuman Ozdaglar. 2009. Distributed subgradient methods for multi-agent optimization. IEEE Trans. on Autom. Control, Vol. 54, 1 (2009), 48--61.
[61]
Angelia Nedić and Asuman Ozdaglar. 2010. Convergence rate for consensus with delays. Journal of Global Optimization, Vol. 47, 3 (2010), 437--456.
[62]
Angelia Nedic, Asuman Ozdaglar, and Pablo A. Parrilo. 2010. Constrained Consensus and Optimization in Multi-Agent Networks. IEEE Trans. Automat. Control, Vol. 55, 4 (2010).
[63]
Feng Niu, Benjamin Recht, Christopher Re, and Stephen J. Wright. 2011. HOGWILD!: A Lock-free Approach to Parallelizing Stochastic Gradient Descent. In Proceedings of the 24th International Conference on Neural Information Processing Systems (NIPS'11).
[64]
Reza Olfati-Saber. 2007. Distributed Kalman filtering for sensor networks. In Proc. of IEEE CDC. 5492--5498.
[65]
Venkata N. Padmanabhan, Helen J. Wang, Philip A. Chou, and Kunwadee Sripanidkulchai. 2002. Distributing streaming media content using cooperative networking. In Proceedings of workshop on Network and operating systems support for digital audio and video. ACM, 177--186.
[66]
Daniel P. Palomar and Mung Chiang. 2007. Alternative distributed algorithms for network utility maximization: Framework and applications. IEEE Trans. on Autom. Control, Vol. 52, 12 (2007), 2254--2269.
[67]
Xinghao Pan, Maximilian Lam, Stephen Tu, Dimitris Papailiopoulos, Ce Zhang, Michael I. Jordan, Kannan Ramchandran, Chris Re, and Benjamin Recht. 2016. CYCLADES: Conflict-free Asynchronous Machine Learning. In Proceedings of the 30th International Conference on Neural Information Processing Systems (NIPS'16).
[68]
Mark A. Paskin, Carlos E. Guestrin, and Jim McFadden. 2005. A robust architecture for distributed inference in sensor networks. In Proceedings of the 4th ACM IPSN.
[69]
David Peleg. 2000. Distributed Computing: A Locality-Sensitive Approach .SIAM Monographs on Discrete Mathematics and Applications.
[70]
Qiuyu Peng and Steven H. Low. 2016. Distributed optimal power flow algorithm for radial networks, I: Balanced single phase case. IEEE Transactions on Smart Grid (2016).
[71]
Robin L Raffard, Claire J Tomlin, and Stephen P Boyd. 2004. Distributed optimization for cooperative agents: Application to formation flight. In Proc. of IEEE Conference on Decision and Control, Vol. 3. 2453--2459.
[72]
Pradeep Ravikumar, Alekh Agarwal, and Martin J. Wainwright. 2010. Message passing for graph-structured linear programs: Proximal methods and rounding schemes. JMLR, Vol. 11 (2010), 1043--1080.
[73]
Omer Reingold and Shai Vardi. 2016. New techniques and tighter bounds for local computation algorithms. Journal of Computer and System Science, Vol. 82, 7 (2016), 1180--1200.
[74]
Ralph Tyrrell Rockafellar. 1984. Network Flows and Monotropic Optimization .John Wiley and Sons, New York.
[75]
Ronitt Rubinfeld, Gil Tamir, Shai Vardi, and Ning Xie. 2011. Fast Local Computation Algorithms. In Proc. 2nd Sym. on Innov. in Computer Science (ICS). 223--238.
[76]
Michael Saks and C. Seshadhri. 2010. Local Monotonicity Reconstruction. SIAM J. on Comp., Vol. 39, 7 (2010), 2897--2926.
[77]
Pedram Samadi, Amir-Hamed Mohsenian-Rad, Robert Schober, Vincent WS Wong, and Juri Jatskevich. 2010. Optimal real-time pricing algorithm based on utility maximization for smart grid. In Proc. of IEEE Smart Grid Communications (SmartGridComm). 415--420.
[78]
Sujay Sanghavi, Dmitry M. Malioutov, and Alan S. Willsky. 2008. Linear programming analysis of loopy belief propagation for weighted matching. In Proc. of NIPS. 1273--1280.
[79]
Ioannis D. Schizas, Alejandro Ribeiro, and Georgios B. Giannakis. 2008. Consensus in ad hoc WSNs with noisy links-Part I: Distributed estimation of deterministic signals. IEEE Trans. on Signal Processing, Vol. 56, 1 (2008), 350--364.
[80]
Shai Shalev-Shwartz, Yoram Singer, Nathan Srebro, and Andrew Cotter. 2011. Pegasos: primal estimated sub-gradient solver for SVM. Mathematical Programming, Vol. 127, 1 (2011), 3--30.
[81]
Wei Shi, Qing Ling, Gang Wu, and Wotao Yin. 2015. A Proximal Gradient Algorithm for Decentralized Composite Optimization. IEEE Transactions on Signal Processing, Vol. 63, 22 (2015).
[82]
Naum Z. Shor. 2012. Minimization methods for non-differentiable functions. Vol. 3. Springer Science & Business Media.
[83]
Rayadurgam Srikant. 2012. The mathematics of Internet congestion control .Springer Science & Business Media.
[84]
Gabriele Steidl and Tanja Teuber. 2010. Removing multiplicative noise by Douglas-Rachford splitting methods. Journal of Math. Imaging and Vision, Vol. 36, 2 (2010), 168--184.
[85]
Ichiro Suzuki and Masafumi Yamashita. 1999. Distributed anonymous mobile robots: Formation of geometric patterns. SIAM J. Comput., Vol. 28, 4 (1999), 1347--1363.
[86]
Håkan Terelius, Ufuk Topcu, and Richard M. Murray. 2011. Decentralized multi-agent optimization via dual decomposition. IEEE Trans. Automat. Control, Vol. 44, 1 (2011).
[87]
John N. Tsitsiklis, Dimitri P. Bertsekas, and Michael Athans. 1986. Distributed asynchronous deterministic and stochastic gradient optimization algorithms. IEEE Trans. on Autom. Control, Vol. 31 (1986), 803--812.
[88]
Ermin Wei, Asuman Ozdaglar, and Ali Jadbabaie. 2015. A distributed Newton method for network utility maximization: Algorithm. IEEE Trans. on Autom. Control, Vol. 58, 9 (2015), 2162--2175.
[89]
David P. Woodruff. 2014. Sketching as a Tool for Numerical Linear Algebra. Found. and Trends in Theoretical Computer Science, Vol. 10, 1--2 (2014), 1--157.
[90]
Yung Yi and Mung Chiang. 2008. Stochastic network utility maximization -- a tribute to Kelly's paper published in this journal a decade ago. European Transactions on Telecommunications, Vol. 19, 4 (2008), 421--442.
[91]
Ruiliang Zhang and James T. Kwok. 2014. Asynchronous Distributed ADMM for Consensus Optimization. In Proceedings of the 31st International Conference on International Conference on Machine Learning - Volume 32 (ICML'14). 1701--1709.

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  • (2023)Virtual Target Based Multi-agent Surrounding Approach2023 19th International Conference on Mobility, Sensing and Networking (MSN)10.1109/MSN60784.2023.00115(786-793)Online publication date: 14-Dec-2023
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  • (2021)Federated BanditProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/34473805:1(1-29)Online publication date: 22-Feb-2021

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cover image Proceedings of the ACM on Measurement and Analysis of Computing Systems
Proceedings of the ACM on Measurement and Analysis of Computing Systems  Volume 3, Issue 3
SIGMETRICS
December 2019
525 pages
EISSN:2476-1249
DOI:10.1145/3376928
Issue’s Table of Contents
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Published: 17 December 2019
Published in POMACS Volume 3, Issue 3

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Author Tags

  1. distributed algorithms
  2. distributed optimization
  3. multi-agent systems

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  • (2023)Virtual Target Based Multi-agent Surrounding Approach2023 19th International Conference on Mobility, Sensing and Networking (MSN)10.1109/MSN60784.2023.00115(786-793)Online publication date: 14-Dec-2023
  • (2022)Accelerating Decentralized Federated Learning in Heterogeneous Edge ComputingIEEE Transactions on Mobile Computing10.1109/TMC.2022.3178378(1-1)Online publication date: 2022
  • (2021)Federated BanditProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/34473805:1(1-29)Online publication date: 22-Feb-2021

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