Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games I: The Ergodic Case

DOI10.1137/19M1274377zbMath1479.65013arXiv1907.05980OpenAlexW3164756548WikidataQ114074243 ScholiaQ114074243MaRDI QIDQ4994415

Mathieu Laurière, René A. Carmona

Publication date: 18 June 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.05980

zbMATH Keywords

rate of convergencenumerical solutionmachine learningergodic mean field controlergodic mean field game

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Neural networks for/in biological studies, artificial life and related topics (92B20) Optimal stochastic control (93E20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) PDEs with randomness, stochastic partial differential equations (35R60) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) 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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Uses Software

• DGM

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