Learning mean-field games with discounted and average costs
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Type :
Article
Publication Status :
Published
Access :
openAccess
Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/
Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/
Abstract
We consider learning approximate Nash equilibria for discrete-time mean-field games with stochastic nonlinear state dynamics subject to both average and discounted costs. To this end, we introduce a mean-field equilibrium (MFE) operator, whose fixed point is a mean-field equilibrium, i.e., equilibrium in the infinite population limit. We first prove that this operator is a contraction, and propose a learning algorithm to compute an approximate mean-field equilibrium by approximating the MFE operator with a random one. Moreover, using the contraction property of the MFE operator, we establish the error analysis of the proposed learning algorithm. We then show that the learned mean-field equilibrium constitutes an approximate Nash equilibrium for finite-agent games.
Source :
Journal of Machine Learning Research
Date :
2023
Volume :
24
Publisher :
Microtome Publishing
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