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
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-02532096
Cahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Laboratoire de Mathématiques d'Orsay [LM-Orsay]
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 / KeywordsMean-field Langevin System; Neural Networks
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