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Convergence of Limited Communications Gradient Methods
KTH, Skolan för elektro- och systemteknik (EES), Nätverk och systemteknik.ORCID-id: 0000-0002-6617-8683
Vise andre og tillknytning
2016 (engelsk)Inngår i: 2016 American Control Conference (ACC), IEEE, 2016, s. 1421-1426Konferansepaper, Publicerat paper (Fagfellevurdert)
Abstract [en]

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.

sted, utgiver, år, opplag, sider
IEEE, 2016. s. 1421-1426
HSV kategori
Forskningsprogram
Elektro- och systemteknik
Identifikatorer
URN: urn:nbn:se:kth:diva-200474DOI: 10.1109/ACC.2016.7525116Scopus ID: 2-s2.0-84992017454OAI: oai:DiVA.org:kth-200474DiVA, id: diva2:1069117
Konferanse
2016 American Control Conference (ACC)
Merknad

QC 20170201

Tilgjengelig fra: 2017-01-27 Laget: 2017-01-27 Sist oppdatert: 2018-12-04bibliografisk kontrollert

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Forlagets fulltekstScopushttp://acc2016.a2c2.org/

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