Learning Optimal Policies in Potential Mean Field Games: Smoothed Policy Iteration Algorithms

DOI10.1137/22m1539861arXiv2212.04791OpenAlexW4391170322WikidataQ129504108 ScholiaQ129504108MaRDI QIDQ6148451

Jiahao Song, Qing Tang

Publication date: 7 February 2024

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.04791

zbMATH Keywords

numerical methodspolicy iterationlearning in gamesmean field games

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Rationality and learning in game theory (91A26) Mean field games (aspects of game theory) (91A16)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Rates of convergence for the policy iteration method for mean field games systems
• Mean field games
• Stable solutions in potential mean field game systems
• Time-dependent focusing mean-field games: the sub-critical case
• Fictitious play property for games with identical interests
• Maximal \(L^q\)-regularity for parabolic Hamilton-Jacobi equations and applications to mean field games
• Mean field games of controls: finite difference approximations
• Short-time existence for a general backward-forward parabolic system arising from mean-field games
• Lipschitz regularity for viscous Hamilton-Jacobi equations with \(L^p\) terms
• Finite mean field games: fictitious play and convergence to a first order continuous mean field game
• Policy iteration method for time-dependent mean field games systems with non-separable Hamiltonians
• Mean Field Games: Convergence of a Finite Difference Method
• Learning in mean field games: The fictitious play
• A policy iteration method for mean field games
• Long time behavior and turnpike solutions in mildly non-monotone mean field games
• Global Properties of Transition Probabilities of Singular Diffusions
• On non-uniqueness and uniqueness of solutions in finite-horizon Mean Field Games
• Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria
• Mean Field Games and Mean Field Type Control Theory
• Probabilistic Theory of Mean Field Games with Applications I
• Mean Field Games: Numerical Methods
• On monotonicity conditions for mean field games

This page was built for publication: Learning Optimal Policies in Potential Mean Field Games: Smoothed Policy Iteration Algorithms