TY - GEN
T1 - Distributed Computation of Wasserstein Barycenters over Networks
AU - Uribe, Cesar A.
AU - Dvinskikh, Darina
AU - Dvurechensky, Pavel
AU - Gasnikov, Alexander
AU - Nedich, Angelia
N1 - Funding Information:
C.A. Uribe (cauribe@mit.edu) is with the Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology. D. Dvinskikh (darina.dvinskikh@wias-berlin.de) is with the Weierstrass Institute for Applied Analysis and Stochastics, and Institute for Information Transmission Problems RAS. P. Dvurechensky (pavel.dvurechensky@wias-berlin.de) is with Weierstrass Institute for Applied Analysis and Stochastics, and Institute for Information Transmission Problems RAS. A. Gasnikov (gasnikov@yandex.ru) is with the Moscow Institute of Physics and Technology, and the Institute for Information Transmission Problems RAS. A. Nedić (angelia.nedich@asu.edu) is with the ECEE Department, Arizona State University, and Moscow Institute of Physics and Technology. The work of A. Gasnikov in Section III-C was supported by the grant of the president of Russian Federation no. MD-1320.2018.1. The work of A. Nedić and C.A. Uribe is supported by the National Science Foundation under grant no. CPS 15-44953. The work of P. Dvurechensky in Section III-C was supported by the grant of the president of Russian Federation no. MK-1806.2017.9. The work of A. Gasnikov and P. Dvurechensky in Sections III-A and III-B was conducted in IITP RAS and supported by the Russian Science Foundation grant (project 14-50-00150).
Publisher Copyright:
© 2018 IEEE.
PY - 2018/7/2
Y1 - 2018/7/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85062181424&partnerID=8YFLogxK
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U2 - 10.1109/CDC.2018.8619160
DO - 10.1109/CDC.2018.8619160
M3 - Conference contribution
AN - SCOPUS:85062181424
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 6544
EP - 6549
BT - 2018 IEEE Conference on Decision and Control, CDC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 57th IEEE Conference on Decision and Control, CDC 2018
Y2 - 17 December 2018 through 19 December 2018
ER -