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Game on Random Environement, Mean-field Langevin System and Neural Networks
In this paper we study a type of games regularized by the relative entro...
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Ergodicity of the underdamped mean-field Langevin dynamics
We study the long time behavior of an underdamped mean-field Langevin (M...
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Mean-Field Learning: a Survey
In this paper we study iterative procedures for stationary equilibria in...
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A mean-field analysis of two-player zero-sum games
Finding Nash equilibria in two-player zero-sum continuous games is a cen...
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Signaling equilibria in mean-field games
In this paper, we consider both finite and infinite horizon discounted d...
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Quantal Response Equilibria in Binary Choice Games on Graphs
Static and dynamic equilibria in noisy binary choice games on graphs are...
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Semi-Explicit Solutions to some Non-Linear Non-Quadratic Mean-Field-Type Games: A Direct Method
This article examines the solvability of mean-field-type game problems b...
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Game on Random Environment, Mean-field Langevin System and Neural Networks
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.
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