Stochastic Generalized Nash Equilibrium-Seeking in Merely Monotone Games

Barbara Franci; Sergio Grammatico

doi:10.1109/TAC.2021.3108496

Stochastic Generalized Nash Equilibrium-Seeking in Merely Monotone Games

Barbara Franci^*, Sergio Grammatico

^*Corresponding author for this work

Research output: Contribution to journal › Article › Scientific › peer-review

11 Citations (Scopus)

42 Downloads (Pure)

Abstract

We solve the stochastic generalized Nash equilibrium (SGNE) problem in merely monotone games with expected value cost functions. Specifically, we present the first distributed SGNE-seeking algorithm for monotone games that require one proximal computation (e.g., one projection step) and one pseudogradient evaluation per iteration. Our main contribution is to extend the relaxed forward–backward operator splitting by the Malitsky (Mathematical Programming, 2019) to the stochastic case and in turn to show almost sure convergence to an SGNE when the expected value of the pseudogradient is approximated by the average over a number of random samples.

Original language	English
Pages (from-to)	3905-3919
Journal	IEEE Transactions on Automatic Control
Volume	67
Issue number	8
DOIs	https://doi.org/10.1109/TAC.2021.3108496
Publication status	Published - 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Stochastic generalized Nash equilibrium problems
stochastic variational inequalities

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10.1109/TAC.2021.3108496

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N2 - We solve the stochastic generalized Nash equilibrium (SGNE) problem in merely monotone games with expected value cost functions. Specifically, we present the first distributed SGNE-seeking algorithm for monotone games that require one proximal computation (e.g., one projection step) and one pseudogradient evaluation per iteration. Our main contribution is to extend the relaxed forward–backward operator splitting by the Malitsky (Mathematical Programming, 2019) to the stochastic case and in turn to show almost sure convergence to an SGNE when the expected value of the pseudogradient is approximated by the average over a number of random samples.

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Stochastic Generalized Nash Equilibrium-Seeking in Merely Monotone Games

Abstract

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Keywords

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