Generalized conditional gradient and learning in potential mean field games

2021/09/13 by J. Frédéric Bonnans, Bonnans, J Frédéric, Pierre Lavigne +3 · 3 citations
Computer Science · Decision Sciences · #Analysis of PDEs (math.AP) #FOS: Mathematics #Game Theory and Applications #Reinforcement Learning in Robotics #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2109.05785

openalex publication_date 2021/09/13 · openalex created_date 2021/09/27 · openalex updated_date 2026/07/28

Abstract

We apply the generalized conditional gradient algorithm to potential mean field games and we show its well-posedeness. It turns out that this method can be interpreted as a learning method called fictitious play. More precisely, each step of the generalized conditional gradient method amounts to compute the best-response of the representative agent, for a predicted value of the coupling terms of the game. We show that for the learning sequence δ_k = 2/(k+2), the potential cost converges in O(1/k), the exploitability and the variables of the problem (distribution, congestion, price, value function and control terms) converge in O(1/√(k)), for specific norms.

Citations

• Learning in anonymous nonatomic games with applications to first-order\n mean field games
• Convergence Analysis of the Frank-Wolfe Algorithm and Its Generalization in Banach Spaces
• Finite mean field games: fictitious play and convergence to a first\n order continuous mean field game
• An entropy minimization approach to second-order variational mean-field\n games
• Scaling up Mean Field Games with Online Mirror Descent
• Mean Field Games Flock! The Reinforcement Learning Way
• Concave Utility Reinforcement Learning: the Mean-Field Game Viewpoint
• Exploration noise for learning linear-quadratic mean field games

Cited by

• Convexifying Mean-Field Control: An Occupation-Measure and Frank-Wolfe Approach
• High-dimensional Mean-Field Games by Particle-based Flow Matching
• Online Episodic Convex Reinforcement Learning

Related

• Generalized conditional gradient and learning in potential mean field games
• Learning in Mean Field Games: the Fictitious Play
• Provable Fictitious Play for General Mean-Field Games
• Mean-Field Learning: a Survey
• Learning optimal policies in potential Mean Field Games: Smoothed Policy Iteration algorithms