Push-Sum Distributed Online Optimization With Bandit Feedback

In this article, we concentrate on distributed online convex optimization problems over multiagent systems, where the communication between nodes is represented by a class of directed graphs that are time varying and uniformly strongly connected. This problem is in bandit feedback, in the sense that...

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Veröffentlicht in:IEEE transactions on cybernetics Jg. 52; H. 4; S. 2263 - 2273
Hauptverfasser: Wang, Cong, Xu, Shengyuan, Yuan, Deming, Zhang, Baoyong, Zhang, Zhengqiang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.04.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
Computational geometry
Convergence
Convex analysis
Convex functions
Convexity
Cost function
Distributed online optimization
Feedback
Graph theory
Graphical representations
Heuristic algorithms
Iterative methods
Multi-agent systems
Multiagent systems
Nodes
one-point bandit feedback
Optimization
push-sum algorithm
ISSN:2168-2267, 2168-2275, 2168-2275
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Zusammenfassung:In this article, we concentrate on distributed online convex optimization problems over multiagent systems, where the communication between nodes is represented by a class of directed graphs that are time varying and uniformly strongly connected. This problem is in bandit feedback, in the sense that at each time only the cost function value at the committed point is revealed to each node. Then, nodes update their decisions by exchanging information with their neighbors only. To deal with Lipschitz continuous and strongly convex cost functions, a distributed online convex optimization algorithm that achieves sublinear individual regret for every node is developed. The algorithm is built on the algorithm called the push-sum scheme that releases the request of doubly stochastic weight matrices, and the one-point gradient estimator that requires the function value at only one point at every iteration, instead of the gradient information of loss function. The expected regret of our proposed algorithm scales as <inline-formula> <tex-math notation="LaTeX">\mathcal {O} (T^{2/3} \ln ^{2/3}(T)) </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">T </tex-math></inline-formula> is the number of iterations. To validate the performance of the algorithm developed in this article, we give a simulation of a common numerical example.
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2020.2999309