Distributed Online Optimization in Dynamic Environments Using Mirror Descent

IEEE Transactions on Automatic Control

Volumn 63, Issue 3, 2018, Pages 714-725

  Shahrampour, Shahin ^a   Jadbabaie, Ali ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

Autonomous systems; distributed optimization; distributed tracking; online learning; time varying optimization

Indexed keywords

DYNAMICS; FUNCTIONS; MIRRORS;

DISTRIBUTED OPTIMIZATION; DYNAMIC ENVIRONMENTS; GLOBAL FUNCTIONS; GLOBAL MINIMIZERS; NETWORK OF AGENTS; NON-STATIONARY ENVIRONMENT; ON-LINE ALGORITHMS; ONLINE OPTIMIZATION;

COST FUNCTIONS;

EID: 85028508233     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2017.2743462     Document Type: Article

References (42)

1. D. Li, K. D. Wong, Y. H. Hu, and A. M. Sayeed, "Detection, classification, and tracking of targets, " IEEE Signal Process. Mag., vol. 19, no. 2, pp. 17-29, Mar. 2002.
2. M. Rabbat and R. Nowak, "Distributed optimization in sensor networks, " in Proc. 3rd Int. Symp. Inf. Process. Sens. Netw., 2004, pp. 20-27.
3. V. Lesser, C. L. Ortiz Jr, and M. Tambe, Distributed Sensor Networks: A multiagent Perspective, vol. 9. New York, NY, USA: Springer, 2012.
4. S. Shahrampour, A. Rakhlin, and A. Jadbabaie, "Distributed detection: Finite-time analysis and impact of network topology, " IEEE Trans. Automat. Control, vol. 61, no. 11, pp. 3256-3268, Nov. 2016.
5. A. Nedic, A. Olshevsky, and C. A. Uribe, "Fast convergence rates for distributed non-Bayesian learning, " IEEE Trans. Automat. Control, 2017, to be published.
6. J. N. Tsitsiklis, "Problems in decentralized decision making and computation, " Ph. D. dissertation, Cambridge, MA, USA, Massachusetts Inst. Technol., 1984.
7. D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods, vol. 23. Englewood Cliffs, NJ, USA: Prentice-Hall, 1989.
8. A. Nedic and A. Ozdaglar, "Distributed subgradient methods for multiagent optimization, " IEEE Trans. Automat. Control, vol. 54, no. 1, pp. 48-61, Jan. 2009.
9. S. S. Ram, A. Nedíc, and V. V. Veeravalli, "Distributed stochastic subgradient projection algorithms for convex optimization, " J. Optim. Theory Appl., vol. 147, no. 3, pp. 516-545, 2010.
10. J. C. Duchi, A. Agarwal, and M. J. Wainwright, "Dual averaging for distributed optimization: Convergence analysis and network scaling, " IEEE Trans. Automat. Control, vol. 57, no. 3, pp. 592-606, Mar. 2012.
11. D. Jakovetíc, J. Xavier, and J. M. Moura, "Fast distributed gradient methods, " IEEE Trans. Automat. Control, vol. 59, no. 5, pp. 1131-1146, May 2014.
12. S. Shalev-Shwartz, "Online learning and online convex optimization, " Found. Trends Mach. Learn., vol. 4, no. 2, pp. 107-194, 2011.
13. M. Zinkevich, "Online convex programming and generalized infinitesimal gradient ascent, " in Proc. Int. Conf. Mach. Learn., 2003, pp. 928-935.
14. E. C. Hall and R. M. Willett, "Online convex optimization in dynamic environments, " IEEE J. Sel. Topics Signal Process., vol. 9, no. 4, pp. 647-662, Jun. 2015.
15. A. Jadbabaie, A. Rakhlin, S. Shahrampour, and K. Sridharan, "Online optimization: Competing with dynamic comparators, " in Proc. 18th Int. Conf. Artif. Intell. Statist., 2015, pp. 398-406.
16. S. Hosseini, A. Chapman, and M. Mesbahi, "Online distributed optimization via dual averaging, " in Proc. IEEE Conf. Decision Control, 2013, pp. 1484-1489.
17. D. Mateos-Núnez and J. Cortés, "Distributed online convex optimization over jointly connected digraphs, " IEEE Trans. Netw. Sci. Eng., vol. 1, no. 1, pp. 23-37, Jan.-Jun. 2014.
18. M. Akbari, B. Gharesifard, and T. Linder, "Distributed online convex optimization on time-varying directed graphs, " IEEE Trans. Control Netw. Syst., 2015, to be published.
19. D. Yudin and A. Nemirovskii, Problem Complexity and Method Efficiency in Optimization. Hoboken, NJ, USA: Wiley, 1983.
20. A. Beck and M. Teboulle, "Mirror descent and nonlinear projected subgradient methods for convex optimization, " Oper. Res. Lett., vol. 31, no. 3, pp. 167-175, 2003.
21. H. H. Bauschke and J. M. Borwein, "Joint and separate convexity of the Bregman distance, " Stud. Comput. Math., vol. 8, pp. 23-36, 2001.
22. J. Li, G. Chen, Z. Dong, and Z. Wu, "Distributed mirror descent method for multi-agent optimization with delay, " Neurocomputing, vol. 177, pp. 643-650, 2016.
23. M. Rabbat, "Multi-agent mirror descent for decentralized stochastic optimization, " in Proc. IEEE 6th Int. Workshop Comput. Adv. Multi-Sens. Adaptive Process., 2015, pp. 517-520.
24. M. Raginsky and J. Bouvrie, "Continuous-time stochastic mirror descent on a network: Variance reduction, consensus, convergence, " in Proc. IEEE Conf. Decision Control, 2012, pp. 6793-6800.
25. A. Nedíc, S. Lee, and M. Raginsky, "Decentralized online optimization with global objectives and local communication, " in Proc. IEEE Amer. Control Conf., 2015, pp. 4497-4503.
26. O. Besbes, Y. Gur, and A. Zeevi, "Non-stationary stochastic optimization, " Oper. Res., vol. 63, no. 5, pp. 1227-1244, 2015.
27. A. Mokhtari, S. Shahrampour, A. Jadbabaie, and A. Ribeiro, "Online optimization in dynamic environments: Improved regret rates for strongly convex problems, " in Proc. IEEE Conf. Decision Control, 2016, pp. 7195-7201.
28. C.-J. Lee, C.-K. Chiang, and M.-E. Wu, "Resisting dynamic strategies in gradually evolving worlds, " in Proc. IEEE 3rd Int. Conf. Robot, Vision Signal Process., 2015, pp. 191-194.
29. M. Fazlyab, S. Paternain, V. M. Preciado, and A. Ribeiro, "Predictioncorrection interior-point method for time-varying convex optimization, " arXiv preprint arXiv:1608. 07544, 2016.
30. A. Simonetto, A. Mokhtari, A. Koppel, G. Leus, and A. Ribeiro, "A class of prediction-correction methods for time-varying convex optimization, " IEEE Trans. Signal Process., vol. 64, no. 17, pp. 4576-4591, Sep. 2016.
31. T. Yang, L. Zhang, R. Jin, and J. Yi, "Tracking slowly moving clairvoyant: Optimal dynamic regret of online learning with true and noisy gradient, " in Proc. 33rd Int. Conf. Mach. Learn., 2016, pp. 449-457.
32. S. Shahrampour and A. Jadbabaie, "An online optimization approach for multi-agent tracking of dynamic parameters in the presence of adversarial noise, " in Proc. IEEE Amer. Control Conf., 2017, pp. 3306-3311.
33. R. Olfati-Saber, "Distributed Kalman filtering for sensor networks, " in Proc. IEEE Conf. Decision Control, 2007, pp. 5492-5498.
34. D. Gu, "Distributed particle filter for target tracking, " in Proc. IEEE Int. Conf. Robot. Autom., 2007, pp. 3856-3861.
35. U. Khan et al., "On connectivity, observability, and stability in distributed estimation, " in Proc. IEEE Conf. Decision Control, 2010, pp. 6639-6644.
36. L. Qipeng, Z. Jiuhua, andW. Xiaofan, "Distributed detection via Bayesian updates and consensus, " in Proc. IEEE 34th Chin. Control Conf., 2015, pp. 6992-6997.
37. L. Zhang, T. Yang, J. Yi, R. Jin, and Z.-H. Zhou, "Improved dynamic regret for non-degeneracy functions, " arXiv preprint arXiv:1608. 03933, 2016.
38. Y. Bar-Shalom, Tracking and Data Association. San Diego, CA, USA: Academic, 1987.
39. D. Acemoglu, A. Nedíc, and A. Ozdaglar, "Convergence of rule-of-thumb learning rules in social networks, " in Proc. IEEE Conf. Decision Control, 2008, pp. 1714-1720.
40. S. Shahrampour, S. Rakhlin, and A. Jadbabaie, "Online learning of dynamic parameters in social networks, " in Proc. 26th Int. Conf. Neural Inf. Process. Syst., 2013, pp. 2013-2021.
41. S. Shahrampour, A. Rakhlin, and A. Jadbabaie, "Distributed estimation of dynamic parameters: Regret analysis, " in Proc. Amer. Control Conf., Jul. 2016, pp. 1066-1071.
42. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U. K.: Cambridge Univ. Press, 2012.