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Convergence of limited communications gradient methods

Publication ,  Conference
Magnússon, S; Heal, K; Enyioha, C; Li, N; Fischione, C; Tarokh, V
Published in: Proceedings of the American Control Conference
July 28, 2016

Distributed control and decision making increasingly play a central role in economical and sustainable operation of cyber-physical systems. Nevertheless, the full potential of the technology has not yet been fully exploited in practice due to communication limitations of real-world infrastructures. This work investigates the fundamental properties of gradient methods for distributed optimization, where gradient information is communicated at every iteration, when using limited number of communicated bits. In particular, a general class of quantized gradient methods are studied where the gradient direction is approximated by a finite quantization set. Conditions on the quantization set are provided that are necessary and sufficient to guarantee the ability of these methods to minimize any convex objective function with Lipschitz continuous gradient and a nonempty, bounded set of optimizers. Moreover, a lower bound on the cardinality of the quantization set is provided, along with specific examples of minimal quantizations. Furthermore, convergence rate results are established that connect the fineness of the quantization and number of iterations needed to reach a predefined solution accuracy. The results provide a bound on the number of bits needed to achieve the desired accuracy. Finally, an application of the theory to resource allocation in power networks is demonstrated, and the theoretical results are substantiated by numerical simulations.

Duke Scholars

Published In

Proceedings of the American Control Conference

DOI

ISSN

0743-1619

Publication Date

July 28, 2016

Volume

2016-July

Start / End Page

1421 / 1426
 

Citation

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Magnússon, S., Heal, K., Enyioha, C., Li, N., Fischione, C., & Tarokh, V. (2016). Convergence of limited communications gradient methods. In Proceedings of the American Control Conference (Vol. 2016-July, pp. 1421–1426). https://doi.org/10.1109/ACC.2016.7525116
Magnússon, S., K. Heal, C. Enyioha, N. Li, C. Fischione, and V. Tarokh. “Convergence of limited communications gradient methods.” In Proceedings of the American Control Conference, 2016-July:1421–26, 2016. https://doi.org/10.1109/ACC.2016.7525116.
Magnússon S, Heal K, Enyioha C, Li N, Fischione C, Tarokh V. Convergence of limited communications gradient methods. In: Proceedings of the American Control Conference. 2016. p. 1421–6.
Magnússon, S., et al. “Convergence of limited communications gradient methods.” Proceedings of the American Control Conference, vol. 2016-July, 2016, pp. 1421–26. Scopus, doi:10.1109/ACC.2016.7525116.
Magnússon S, Heal K, Enyioha C, Li N, Fischione C, Tarokh V. Convergence of limited communications gradient methods. Proceedings of the American Control Conference. 2016. p. 1421–1426.

Published In

Proceedings of the American Control Conference

DOI

ISSN

0743-1619

Publication Date

July 28, 2016

Volume

2016-July

Start / End Page

1421 / 1426