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Game on Random Environement, Mean-field Langevin System and Neural Networks

Conforti, Giovanni; Kazeykina, Anna; Ren, Zhenjie (2020), Game on Random Environement, Mean-field Langevin System and Neural Networks. https://basepub.dauphine.fr/handle/123456789/20613

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02532096
Date
2020
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
24
Metadata
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Author(s)
Conforti, Giovanni
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Kazeykina, Anna
Laboratoire de Mathématiques d'Orsay [LM-Orsay]
Ren, Zhenjie
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
In this paper we study a type of games regularized by the relative entropy, where the players' strategies are coupled through a random environment variable. Besides the existence and the uniqueness of equilibria of such games, we prove that the marginal laws of the corresponding mean-field Langevin systems can converge towards the games' equilibria in different settings. As applications, the dynamic games can be treated as games on a random environment when one treats the time horizon as the environment. In practice, our results can be applied to analysing the stochastic gradient descent algorithm for deep neural networks in the context of supervised learning as well as for the generative adversarial networks.
Subjects / Keywords
Mean-field Langevin System; Neural Networks

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