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One of the core problems in mean-field control and mean-field games is to solve the corresponding McKean-Vlasov forward-backward stochastic differential equations (MV-FBSDEs).
Some notes on computation of games solutions
George W Brown · 1949
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Iterative solution of games by fictitious play
George W Brown · 1951
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Integral probability metrics and their generating classes of functions
Alfred Müller · 1997
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Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
Minyi Huang, Peter E Caines, and Roland P Malhamé · 2006
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Jeux à champ moyen. I. Le cas stationnaire
Jean-Michel Lasry and Pierre-Louis Lions · 2006
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Jeux à champ moyen. II. Horizon fini et contrôle optimal
Jean-Michel Lasry and Pierre-Louis Lions · 2006
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On the mathematics of emergence
Felipe Cucker and Steve Smale · 2007
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Large-population cost-coupled LQG problems with nonuniform agents: Individual-mass behavior and decentralized ϵ \epsilon -Nash equilibria
Minyi Huang, Peter E Caines, and Roland P Malhamé · 2007
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Mean field games
Jean-Michel Lasry and Pierre-Louis Lions · 2007
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Théorie des jeuxa champs moyen et applications
PL Lions · 2007
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Time discretization and markovian iteration for coupled FBSDEs
Christian Bender and Jianfeng Zhang · 2008
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Synthesis of cucker-smale type flocking via mean field stochastic control theory: Nash equilibria
Mojtaba Nourian, Peter E Caines, and Roland P Malhamé · 2010
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Mean field analysis of controlled cucker-smale type flocking: Linear analysis and perturbation equations
Mojtaba Nourian, Peter E Caines, and Roland P Malhamé · 2011
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Mean field forward-backward stochastic differential equations
René Carmona and François Delarue · 2013
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Probabilistic analysis of mean-field games
René Carmona and François Delarue · 2013
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Forward–backward stochastic differential equations and controlled McKean–Vlasov dynamics
René Carmona and François Delarue · 2015
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A cubature based algorithm to solve decoupled McKean–Vlasov forward–backward stochastic differential equations
PE Chaudru de Raynal and CA Garcia Trillos · 2015
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Wasserstein generative adversarial networks
M. Arjovsky, S. Chintala, and L. Bottou · 2017
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Probabilistic Theory of Mean Field Games with Applications I
René Carmona and François Delarue · 2017
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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
Weinan E, Jiequn Han, and Arnulf Jentzen · 2017
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Improved training of Wasserstein GANs
I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, and A. C. Courville · 2017
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Backward Stochastic Differential Equations
Jianfeng Zhang · 2017
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Lipschitz regularized deep neural networks generalize and are adversarially robust
Convergence of the deep BSDE method for coupled FBSDEs
Jiequn Han and Jihao Long · 2020
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Deep backward schemes for high-dimensional nonlinear pdes
Côme Huré, Huyên Pham, and Xavier Warin · 2020
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Path regularity of coupled McKean-Vlasov FBSDEs
Christoph Reisinger, Wolfgang Stockinger, and Yufei Zhang · 2020
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A machine learning framework for solving high-dimensional mean field game and mean field control problems
Lars Ruthotto, Stanley J Osher, Wuchen Li, Levon Nurbekyan, and Samy Wu Fung · 2020
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Provable fictitious play for general mean-field games
Qiaomin Xie, Zhuoran Yang, Zhaoran Wang, and Andreea Minca · 2020
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Chris Finlay, Jeff Calder, Bilal Abbasi, and Adam Oberman · 2018
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Solving high-dimensional partial differential equations using deep learning
Jiequn Han, Arnulf Jentzen, and Weinan E · 2018
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René Carmona and Mathieu Laurière · 2019
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Numerical method for FBSDEs of McKean–Vlasov type
Jean-François Chassagneux, Dan Crisan, and François Delarue · 2019
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The Barron space and the flow-induced function spaces for neural network models
Weinan E, Chao Ma, and Lei Wu · 2019
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Efficient and accurate estimation of Lipschitz constants for deep neural networks
M. Fazlyab, A. Robey, H. Hassani, M. Morari, and G. Pappas · 2019
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Numerical resolution of McKean-Vlasov FBSDEs using neural networks
Maximilien Germain, Joseph Mikael, and Xavier Warin · 2019
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Convergence of some mean field games systems to aggregation and flocking models
Martino Bardi and Pierre Cardaliaguet · 2021
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A class of dimensionality-free metrics for the convergence of empirical measures
Jiequn Han, Ruimeng Hu, and Jihao Long · 2021
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Deepham: A global solution method for heterogeneous agent models with aggregate shocks
Jiequn Han, Yucheng Yang, and Weinan E · 2021
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Deep fictitious play for stochastic differential games
Ruimeng Hu · 2021
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Signatured deep fictitious play for mean field games with common noise
Ming Min and Ruimeng Hu · 2021
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Training robust neural networks using Lipschitz bounds
Patricia Pauli, Anne Koch, Julian Berberich, Paul Kohler, and Frank Allgöwer · 2021
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Mean field games flock! the reinforcement learning way
Sarah Perrin, Mathieu Laurière, Julien Pérolat, Matthieu Geist, Romuald Élie, and Olivier Pietquin · 2021
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A fast iterative PDE-based algorithm for feedback controls of nonsmooth mean-field control problems
Christoph Reisinger, Wolfgang Stockinger, and Yufei Zhang · 2021
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A Cucker–Smale inspired deterministic mean field game with velocity interactions
Filippo Santambrogio and Woojoo Shim · 2021
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Optimal policies for a pandemic: A stochastic game approach and a deep learning algorithm
Yao Xuan, Robert Balkin, Jiequn Han, Ruimeng Hu, and Hector D. Ceniceros · 2021
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Income and wealth distribution in macroeconomics: A continuous-time approach
Yves Achdou, Jiequn Han, Jean-Michel Lasry, Pierre-Louis Lions, and Benjamin Moll · 2022
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