Convergence analysis of machine learning algorithms for the numerical solution of mean field control and games. II: The finite horizon case

DOI10.1214/21-AAP1715zbMath1505.65243arXiv1908.01613MaRDI QIDQ2108885

Mathieu Laurière, René A. Carmona

Publication date: 20 December 2022

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.01613

zbMATH Keywords

numerical approximationmachine learningmean field gamesforward-backward SDEmean field controlMcKean-Vlasov

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Neural networks for/in biological studies, artificial life and related topics (92B20) Optimal stochastic control (93E20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) PDEs with randomness, stochastic partial differential equations (35R60) Numerical solutions to stochastic differential and integral equations (65C30) Vlasov equations (35Q83) PDEs in connection with control and optimization (35Q93) Mean field games and control (49N80) Mean field games (aspects of game theory) (91A16) PDEs in connection with mean field game theory (35Q89)

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