### Abstract

We study the decentralized distributed computation of discrete approximations for the regularized Wasserstein barycenter of a finite set of continuous probability measures distributedly stored over a network. We assume there is a network of agents/machines/computers, and each agent holds a private continuous probability measure and seeks to compute the barycenter of all the measures in the network by getting samples from its local measure and exchanging information with its neighbors. Motivated by this problem, we develop, and analyze, a novel accelerated primal-dual stochastic gradient method for general stochastic convex optimization problems with linear equality constraints. Then, we apply this method to the decentralized distributed optimization setting to obtain a new algorithm for the distributed semi-discrete regularized Wasserstein barycenter problem. Moreover, we show explicit non-asymptotic complexity for the proposed algorithm. Finally, we show the effectiveness of our method on the distributed computation of the regularized Wasserstein barycenter of univariate Gaussian and von Mises distributions, as well as some applications to image aggregation.
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Original language | English (US) |
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Pages (from-to) | 10760-10770 |

Number of pages | 11 |

Journal | Advances in Neural Information Processing Systems |

Volume | 2018-December |

State | Published - Jan 1 2018 |

Event | 32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada Duration: Dec 2 2018 → Dec 8 2018 |

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### ASJC Scopus subject areas

- Computer Networks and Communications
- Information Systems
- Signal Processing

### Cite this

*Advances in Neural Information Processing Systems*,

*2018-December*, 10760-10770.

**Decentralize and randomize : Faster algorithm for Wasserstein barycenters.** / Dvurechensky, Pavel; Dvinskikh, Darina; Gasnikov, Alexander; Uribe, César A.; Nedich, Angelia.

Research output: Contribution to journal › Conference article

*Advances in Neural Information Processing Systems*, vol. 2018-December, pp. 10760-10770.

}

TY - JOUR

T1 - Decentralize and randomize

T2 - Faster algorithm for Wasserstein barycenters

AU - Dvurechensky, Pavel

AU - Dvinskikh, Darina

AU - Gasnikov, Alexander

AU - Uribe, César A.

AU - Nedich, Angelia

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We study the decentralized distributed computation of discrete approximations for the regularized Wasserstein barycenter of a finite set of continuous probability measures distributedly stored over a network. We assume there is a network of agents/machines/computers, and each agent holds a private continuous probability measure and seeks to compute the barycenter of all the measures in the network by getting samples from its local measure and exchanging information with its neighbors. Motivated by this problem, we develop, and analyze, a novel accelerated primal-dual stochastic gradient method for general stochastic convex optimization problems with linear equality constraints. Then, we apply this method to the decentralized distributed optimization setting to obtain a new algorithm for the distributed semi-discrete regularized Wasserstein barycenter problem. Moreover, we show explicit non-asymptotic complexity for the proposed algorithm. Finally, we show the effectiveness of our method on the distributed computation of the regularized Wasserstein barycenter of univariate Gaussian and von Mises distributions, as well as some applications to image aggregation. 1

AB - We study the decentralized distributed computation of discrete approximations for the regularized Wasserstein barycenter of a finite set of continuous probability measures distributedly stored over a network. We assume there is a network of agents/machines/computers, and each agent holds a private continuous probability measure and seeks to compute the barycenter of all the measures in the network by getting samples from its local measure and exchanging information with its neighbors. Motivated by this problem, we develop, and analyze, a novel accelerated primal-dual stochastic gradient method for general stochastic convex optimization problems with linear equality constraints. Then, we apply this method to the decentralized distributed optimization setting to obtain a new algorithm for the distributed semi-discrete regularized Wasserstein barycenter problem. Moreover, we show explicit non-asymptotic complexity for the proposed algorithm. Finally, we show the effectiveness of our method on the distributed computation of the regularized Wasserstein barycenter of univariate Gaussian and von Mises distributions, as well as some applications to image aggregation. 1

UR - http://www.scopus.com/inward/record.url?scp=85064808215&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064808215&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:85064808215

VL - 2018-December

SP - 10760

EP - 10770

JO - Advances in Neural Information Processing Systems

JF - Advances in Neural Information Processing Systems

SN - 1049-5258

ER -