Mathieu Laurière
Princeton University
103 Papers
265 Citations
Mathieu Laurière is an academic researcher from Princeton University. The author has contributed to research in topics: Computer science & Nash equilibrium. The author has an hindex of 17, co-authored 83 publications. Previous affiliations of Mathieu Laurière include Pierre-and-Marie-Curie University & Paris Diderot University.
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Papers
•Posted Content
Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: I -- The Ergodic Case
René Carmona,Mathieu Laurière +1 more
TL;DR: Two algorithms are proposed for the solution of the optimal control of ergodic McKean-Vlasov dynamics based on the approximation of the theoretical solutions by neural networks, which allows the use of modern machine learning tools, and efficient implementations of stochastic gradient descent.
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Numerical methods for mean field games and mean field type control
Mathieu Laurière
- 01 Jan 2021
TL;DR: Numerical schemes for forward-backward systems of partial differential equations (PDEs), optimization techniques for variational problems driven by a Kolmogorov-Fokker-Planck PDE, an approach based on a monotone operator viewpoint, and stochastic methods relying on machine learning tools are discussed.
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•Posted Content
Model-Free Mean-Field Reinforcement Learning: Mean-Field MDP and Mean-Field Q-Learning
TL;DR: This work introduces generic model-free algorithms based on the state-action value function at the mean field level and proves convergence for a prototypical Q-learning method for mean field control problems.
Mean Field Games and Applications: Numerical Aspects
Yves Achdou,Mathieu Laurière +1 more
TL;DR: In this survey, several aspects of a finite difference method used to approximate the previously mentioned system of PDEs are discussed, including convergence, variational aspects and algorithms for solving the resulting systems of nonlinear equations.
Dynamic Programming for Mean-Field Type Control
TL;DR: A Hamilton–Jacobi–Bellman fixed-point algorithm is compared to a steepest descent method issued from calculus of variations and an extended Bellman’s principle is derived by a different argument.