Distributed Computation of Wasserstein Barycenters over Networks

Cesar A. Uribe, Darina Dvinskikh, Pavel Dvurechensky, Alexander Gasnikov, Angelia Nedich

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We propose a new class-optimal algorithm for the distributed computation of Wasserstein Barycenters over networks. Assuming that each node in a graph has a probability distribution, we prove that every node reaches the barycenter of all distributions held in the network by using local interactions compliant with the topology of the graph. We provide an estimate for the minimum number of communication rounds required for the proposed method to achieve arbitrary relative precision both in the optimality of the solution and the consensus among all agents for undirected fixed networks.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6544-6549
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Distributed Computation
Barycentre
Probability distributions
Topology
Communication
Relative Precision
Local Interaction
Graph in graph theory
Vertex of a graph
Optimal Algorithm
Optimality
Probability Distribution
Arbitrary
Estimate

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Uribe, C. A., Dvinskikh, D., Dvurechensky, P., Gasnikov, A., & Nedich, A. (2019). Distributed Computation of Wasserstein Barycenters over Networks. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 6544-6549). [8619160] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619160

Distributed Computation of Wasserstein Barycenters over Networks. / Uribe, Cesar A.; Dvinskikh, Darina; Dvurechensky, Pavel; Gasnikov, Alexander; Nedich, Angelia.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 6544-6549 8619160 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Uribe, CA, Dvinskikh, D, Dvurechensky, P, Gasnikov, A & Nedich, A 2019, Distributed Computation of Wasserstein Barycenters over Networks. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619160, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 6544-6549, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8619160
Uribe CA, Dvinskikh D, Dvurechensky P, Gasnikov A, Nedich A. Distributed Computation of Wasserstein Barycenters over Networks. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 6544-6549. 8619160. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8619160
Uribe, Cesar A. ; Dvinskikh, Darina ; Dvurechensky, Pavel ; Gasnikov, Alexander ; Nedich, Angelia. / Distributed Computation of Wasserstein Barycenters over Networks. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 6544-6549 (Proceedings of the IEEE Conference on Decision and Control).
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