Online Learning Over Dynamic Graphs via Distributed Proximal Gradient Algorithm

We consider the problem of tracking the minimum of a time-varying convex optimization problem over a dynamic graph. Motivated by target tracking and parameter estimation problems in intermittently connected robotic and sensor networks, the goal is to design a distributed algorithm capable of handlin...

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Vydáno v:IEEE transactions on automatic control Ročník 66; číslo 11; s. 5065 - 5079
Hlavní autoři: Dixit, Rishabh, Bedi, Amrit Singh, Rajawat, Ketan
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.11.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Computational geometry
Convexity
Distributed algorithms
Distributed optimization
dynamic regret
Empirical analysis
Graphs
Machine learning
Network topologies
Network topology
online convex optimization
Optimization
Parameter estimation
Regularization
sparse signal recovery
Time-varying systems
Tracking
ISSN:0018-9286, 1558-2523
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Shrnutí:We consider the problem of tracking the minimum of a time-varying convex optimization problem over a dynamic graph. Motivated by target tracking and parameter estimation problems in intermittently connected robotic and sensor networks, the goal is to design a distributed algorithm capable of handling nondifferentiable regularization penalties. The proposed proximal online gradient descent algorithm is built to run in a fully decentralized manner and utilizes consensus updates over possibly disconnected graphs. The performance of the proposed algorithm is analyzed by developing bounds on its dynamic regret in terms of the cumulative path length of the time-varying optimum. It is shown that as compared to the centralized case, the dynamic regret incurred by the proposed algorithm over <inline-formula><tex-math notation="LaTeX">T</tex-math></inline-formula> time slots is worse by a factor of <inline-formula><tex-math notation="LaTeX">\log (T)</tex-math></inline-formula> only, despite the disconnected and time-varying network topology. The empirical performance of the proposed algorithm is tested on the distributed dynamic sparse recovery problem, where it is shown to incur a dynamic regret that is close to that of the centralized algorithm.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2020.3033712