Learning over multitask graphs-part II: performance analysis
File(s)
Author(s)
Nassif, Roula
Vlaski, Stefan
Richard, Cedric
Sayed, Ali H
Type
Journal Article
Abstract
Part I of this paper formulated a multitask optimization problem where agents in the network
have individual objectives to meet, or individual parameter vectors to estimate, subject to a smoothness
condition over the graph. A diffusion strategy was devised that responds to streaming data and employs
stochastic approximations in place of actual gradient vectors, which are generally unavailable. The approach
relied on minimizing a global cost consisting of the aggregate sum of individual costs regularized by a term
that promotes smoothness. We examined the first-order, the second-order, and the fourth-order stability of
the multitask learning algorithm. The results identified conditions on the step-size parameter, regularization
strength, and data characteristics in order to ensure stability. This Part II examines steady-state performance
of the strategy. The results reveal explicitly the influence of the network topology and the regularization
strength on the network performance and provide insights into the design of effective multitask strategies for
distributed inference over networks.
have individual objectives to meet, or individual parameter vectors to estimate, subject to a smoothness
condition over the graph. A diffusion strategy was devised that responds to streaming data and employs
stochastic approximations in place of actual gradient vectors, which are generally unavailable. The approach
relied on minimizing a global cost consisting of the aggregate sum of individual costs regularized by a term
that promotes smoothness. We examined the first-order, the second-order, and the fourth-order stability of
the multitask learning algorithm. The results identified conditions on the step-size parameter, regularization
strength, and data characteristics in order to ensure stability. This Part II examines steady-state performance
of the strategy. The results reveal explicitly the influence of the network topology and the regularization
strength on the network performance and provide insights into the design of effective multitask strategies for
distributed inference over networks.
Date Issued
2020
Date Acceptance
2020-04-14
Citation
IEEE Open Journal of Signal Processing, 2020, 1, pp.46-63
ISSN
2644-1322
Publisher
IEEE
Start Page
46
End Page
63
Journal / Book Title
IEEE Open Journal of Signal Processing
Volume
1
Copyright Statement
CCBY - IEEE is not the copyright holder of this material. Please follow the instructions via https://creativecommons.org/licenses/by/4.0/ to obtain full-text articles and stipulations in the API documentation.
License URL
Identifier
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Subjects
ALGORITHMS
BEHAVIOR
diffusion strategy
Engineering
Engineering, Electrical & Electronic
gradient noise
graph Laplacian regularization
LMS
Multitask distributed inference
NETWORKS
Science & Technology
smoothness prior
steady-state performance
Technology
Publication Status
Published
Date Publish Online
2020-04-21