Decentralized Optimization in Time-Varying Networks with Arbitrary Delays

Fuente: arXiv
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Main Authors: Ortega, Tomas, Jafarkhani, Hamid
Format: Preprint
Published: 2024
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author Ortega, Tomas
Jafarkhani, Hamid
author_facet Ortega, Tomas
Jafarkhani, Hamid
contents We consider a decentralized optimization problem for networks affected by communication delays. Examples of such networks include collaborative machine learning, sensor networks, and multi-agent systems. To mimic communication delays, we add virtual non-computing nodes to the network, resulting in directed graphs. This motivates investigating decentralized optimization solutions on directed graphs. Existing solutions assume nodes know their out-degrees, resulting in limited applicability. To overcome this limitation, we introduce a novel gossip-based algorithm, called DT-GO, that does not need to know the out-degrees. The algorithm is applicable in general directed networks, for example networks with delays or limited acknowledgment capabilities. We derive convergence rates for both convex and non-convex objectives, showing that our algorithm achieves the same complexity order as centralized Stochastic Gradient Descent. In other words, the effects of the graph topology and delays are confined to higher-order terms. Additionally, we extend our analysis to accommodate time-varying network topologies. Numerical simulations are provided to support our theoretical findings.
format Preprint
id arxiv_https___arxiv_org_abs_2405_19513
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Decentralized Optimization in Time-Varying Networks with Arbitrary Delays
Ortega, Tomas
Jafarkhani, Hamid
Machine Learning
Distributed, Parallel, and Cluster Computing
Systems and Control
Optimization and Control
68W10, 68W15, 68W40, 90C06, 90C35, 90C25
G.1.6; F.2.1; E.4
We consider a decentralized optimization problem for networks affected by communication delays. Examples of such networks include collaborative machine learning, sensor networks, and multi-agent systems. To mimic communication delays, we add virtual non-computing nodes to the network, resulting in directed graphs. This motivates investigating decentralized optimization solutions on directed graphs. Existing solutions assume nodes know their out-degrees, resulting in limited applicability. To overcome this limitation, we introduce a novel gossip-based algorithm, called DT-GO, that does not need to know the out-degrees. The algorithm is applicable in general directed networks, for example networks with delays or limited acknowledgment capabilities. We derive convergence rates for both convex and non-convex objectives, showing that our algorithm achieves the same complexity order as centralized Stochastic Gradient Descent. In other words, the effects of the graph topology and delays are confined to higher-order terms. Additionally, we extend our analysis to accommodate time-varying network topologies. Numerical simulations are provided to support our theoretical findings.
title Decentralized Optimization in Time-Varying Networks with Arbitrary Delays
topic Machine Learning
Distributed, Parallel, and Cluster Computing
Systems and Control
Optimization and Control
68W10, 68W15, 68W40, 90C06, 90C35, 90C25
G.1.6; F.2.1; E.4
url https://arxiv.org/abs/2405.19513