### 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 language | English (US) |
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Title of host publication | 2018 IEEE Conference on Decision and Control, CDC 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 6544-6549 |

Number of pages | 6 |

ISBN (Electronic) | 9781538613955 |

DOIs | |

State | Published - Jan 18 2019 |

Event | 57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: Dec 17 2018 → Dec 19 2018 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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Volume | 2018-December |

ISSN (Print) | 0743-1546 |

### Conference

Conference | 57th IEEE Conference on Decision and Control, CDC 2018 |
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Country | United States |

City | Miami |

Period | 12/17/18 → 12/19/18 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

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

PY - 2019/1/18

Y1 - 2019/1/18

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.

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UR - http://www.scopus.com/inward/citedby.url?scp=85062181424&partnerID=8YFLogxK

U2 - 10.1109/CDC.2018.8619160

DO - 10.1109/CDC.2018.8619160

M3 - Conference contribution

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.

ER -