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We develop an exhaustive study of Markov decision process (MDP) under mean field interaction both on states and actions in the presence of common noise, and when optimization is performed over open-loop controls on infinite horizon.
Weak convergence of empirical processes
A. Van der Vaart and J.A. Wellner · 1996
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Mass transportation problems
S.T. Rachev and L. Rüschendorf · 1998
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Foundations of Modern Probability
O. Kallenberg · 2002
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C. Villani · 2009
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Measurability of optimal transportation and strong coupling of martingale measures
J. Fontbana, H. Guérin, and S. Méléard · 2010
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Dynamic programming and optimal control, Vol II, approximate dynamic programming
D. P. Bertsekas · 2012
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Mean field games and mean field type control theory
A. Bensoussan, J. Frehse, and P. Yam · 2013
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On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
E. Boissard and T. Le Gouic · 2014
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On the rate of convergence in Wasserstein distance of the empirical measure
N. Fournier and A. Guillin · 2015
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Dynamic programming for mean-field type controls
M. Laurière and O. Pironneau · 2016
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Discrete time McKean-Vlasov control problem: a dynamic programming approach
H. Pham and X. Wei · 2016
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Limit theory for controlled McKean-Vlasov dynamics
D. Lacker · 2017
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Dynamic programming for optimal control of stochastic McKean-Vlasov dynamics
H. Pham and X. Wei · 2017
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Reinforcement learning: an introduction
R.S. Sutton and A.G. Barto · 2017
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Mean-field optimal control as Gamma-limit of finite agent controls
M. Fornasier, S. Lisini, C. Orrieri, and G. Savaré · 2018
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Model-free mean-field reinforcement learning: mean-field MDP and mean-field Q-learning
R. Carmona, M. Laurière, and Z. Tan · 2019
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McKean-Vlasov optimal control: the dynamic programming principle
M.F. Djete, D. Possamai, and X. Tan · 2019
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Dynamic programming principles for learning MFCs
H. Gu, X. Guo, X. Wei, and R. Xu · 2019
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Learning mean-field games
X. Guo, A. Hu, R. Xu, and J. Zhang · 2019
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Extended mean field control problem: a propagation of chaos result
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Randomized dynamic programming principle and Feynman-Kac representation for optimal control of McKean-Vlasov dynamics
E. Bayraktar, A. Cosso, and H. Pham · 2018
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Probabilistic Theory of Mean Field Games with Applications vol I. and II
R. Carmona and F. Delarue · 2018
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M.F. Djete · 2020
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Convergence of large population games to mean field games with interaction through the controls
M. Laurière and L. Tangpi · 2020
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