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DIMIX: Diminishing Mixing for Sloppy Agents

We study nonconvex distributed optimization problems where a set of agents collaboratively solve a separable optimization problem that is distributed over a time-varying network. The existing methods to solve these problems rely on (at most) one-time-scale algorithms, where each agent performs a diminishing or constant step-size gradient descent at the average estimate of the agents in the network. However, if possible at all, exchanging exact information, which is required to evaluate these average estimates, potentially introduces a massive communication overhead. Therefore, a reasonable practical assumption to be made is that agents only receive a rough approximation of the neighboring agents’ information. To address this, we introduce and study a two-time-scale decentralized algorithm with a broad class of lossy information sharing methods (which includes noisy, quantized, and/or compressed information sharing) over time-varying networks. In our method, one time-scale suppresses the (imperfect) incoming information from the neighboring agents, and one time-scale operates on local cost functions’ gradients. We show that with a proper choices for the step-sizes’ parameters, the algorithm achieves a convergence rate of
for nonconvex distributed optimization problems over time-varying networks for any .

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON OPTIMIZATION; Vol.33 No.2 April-June 2023

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 978-1005

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

DISTRIBUTED OPTIMIZATION
NONCONVEX OPTIMIZATION
TIME-VARYING GRAPHS
DISTRIBUTED MULTIAGENT SYSTEM
GRADIENT DESCENT ALGORITHMS

Info Detail Spesifik

https://doi.org/10.1137/21M143546X

Pernyataan Tanggungjawab

Hadi Reisizadeh, Behrouz Touri, Soheil Mohajer

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