A damped forward-backward algorithm for stochastic generalized Nash equilibrium seeking

We consider a stochastic generalized Nash equilibrium problem (GNEP) with expected-value cost functions. Inspired by Yi and Pavel (Automatica, 2019), we propose a distributed GNE seeking algorithm by exploiting the forward- backward operator splitting and a suitable preconditioning matrix. Specifica...

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Vydané v:2020 European Control Conference (ECC) s. 1117 - 1122
Hlavní autori: Franci, Barbara, Grammatico, Sergio
Médium: Konferenčný príspevok..
Jazyk:English
Vydavateľské údaje: EUCA 01.05.2020
Predmet:
Convergence
Cost function
Games
Nash equilibrium
Random variables
Stochastic processes
Uncertainty
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Shrnutí:We consider a stochastic generalized Nash equilibrium problem (GNEP) with expected-value cost functions. Inspired by Yi and Pavel (Automatica, 2019), we propose a distributed GNE seeking algorithm by exploiting the forward- backward operator splitting and a suitable preconditioning matrix. Specifically, we apply this method to the stochastic GNEP, where, at each iteration, the expected value of the pseudo-gradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of our proposed algorithm if the sample size grows large enough.
DOI:10.23919/ECC51009.2020.9143966