Distributed stochastic Nash equilibrium seeking under heavy-tailed noises

This paper studies the distributed stochastic Nash equilibrium seeking problem under heavy-tailed noises. Unlike the traditional stochastic Nash equilibrium algorithms, where the gradient noises are usually assumed to have a bounded variance, we assume that the gradient noises can be heavy-tailed, w...

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Vydané v:	Automatica (Oxford) Ročník 173; s. 112081
Hlavní autori:	Sun, Chao, Chen, Bo, Wang, Jianzheng, Wang, Zheming, Yu, Li
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Ltd 01.03.2025
Predmet:	Distributed algorithms Nash equilibrium seeking Stochastic algorithms Stochastic algorithms Distributed algorithms Nash equilibrium seeking
ISSN:	0005-1098
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Popis
Shrnutí:	This paper studies the distributed stochastic Nash equilibrium seeking problem under heavy-tailed noises. Unlike the traditional stochastic Nash equilibrium algorithms, where the gradient noises are usually assumed to have a bounded variance, we assume that the gradient noises can be heavy-tailed, which can have an unbounded variance. A distributed Nash equilibrium seeking law combining projected gradient descent and gradient clipping is proposed. Sufficient conditions on the step-sizes are given to guarantee almost sure and in mean square convergence to the Nash equilibrium of the game. A numerical example is given to show the effectiveness and efficiency of the algorithm.
ISSN:	0005-1098
DOI:	10.1016/j.automatica.2024.112081