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We study convergence rates of the generalized conditional gradient (GCG) method applied to fully discretized Mean Field Games (MFG) systems. While explicit convergence rates of the GCG method have been established at the continuous PDE…

Numerical Analysis · Mathematics 2026-02-13 Haruka Nakamura , Norikazu Saito

We consider infinite horizon dynamic programming problems, where the control at each stage consists of several distinct decisions, each one made by one of several agents. In an earlier work we introduced a policy iteration algorithm, where…

Optimization and Control · Mathematics 2020-05-05 Dimitri Bertsekas

We establish the convergence of the deep actor-critic reinforcement learning algorithm presented in [Angiuli et al., 2023a] in the setting of continuous state and action spaces with an infinite discrete-time horizon. This algorithm provides…

Optimization and Control · Mathematics 2025-11-11 Jean-Pierre Fouque , Mathieu Laurière , Mengrui Zhang

Stochastic games provide a framework for interactions among multiple agents and enable a myriad of applications. In these games, agents decide on actions simultaneously, the state of every agent moves to the next state, and each agent…

Machine Learning · Computer Science 2019-10-10 Mridul Agarwal , Vaneet Aggarwal , Arnob Ghosh , Nilay Tiwari

This paper builds on the work of Degond, Herty and Liu by considering N-player stochastic differential games. The control corresponding to a Nash equilibrium of such a game is approximated through model predictive control (MPC) techniques.…

Optimization and Control · Mathematics 2019-11-12 Matt Barker

We establish the convergence of the unified two-timescale Reinforcement Learning (RL) algorithm presented in a previous work by Angiuli et al. This algorithm provides solutions to Mean Field Game (MFG) or Mean Field Control (MFC) problems…

Optimization and Control · Mathematics 2024-05-02 Andrea Angiuli , Jean-Pierre Fouque , Mathieu Laurière , Mengrui Zhang

Game-theoretic models are effective tools for modeling multi-agent interactions, especially when robots need to coordinate with humans. However, applying these models requires inferring their specifications from observed behaviors -- a…

Robotics · Computer Science 2025-02-06 Max Muchen Sun , Pete Trautman , Todd Murphey

We propose an efficient solution approach for high-dimensional nonlocal mean-field game (MFG) systems based on the Monte Carlo approximation of interaction kernels via random features. We avoid costly space-discretizations of interaction…

Numerical Analysis · Mathematics 2022-07-26 Sudhanshu Agrawal , Wonjun Lee , Samy Wu Fung , Levon Nurbekyan

This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization…

Optimization and Control · Mathematics 2023-08-29 Xin Guo , Anran Hu , Junzi Zhang

Mean field games (MFGs) model interactions in large-population multi-agent systems through population distributions. Traditional learning methods for MFGs are based on fixed-point iteration (FPI), where policy updates and induced population…

Machine Learning · Computer Science 2025-02-17 Chenyu Zhang , Xu Chen , Xuan Di

A common technique in reinforcement learning is to evaluate the value function from Monte Carlo simulations of a given policy, and use the estimated value function to obtain a new policy which is greedy with respect to the estimated value…

Machine Learning · Computer Science 2023-03-01 Anna Winnicki , R. Srikant

In this paper, linear quadratic mean field games (LQMFGs) under heterogeneous erroneous initial information are investigated, focusing on how to achieve error correction by calculation based on the agents' own actual state and interactions…

Optimization and Control · Mathematics 2025-04-08 Yuxin Jin , Lu Ren , Wang Yao , Xiao Zhang

In this article we consider finite Mean Field Games (MFGs), i.e. with finite time and finite states. We adopt the framework introduced in Gomes Mohr and Souza in 2010, and study two seemly unexplored subjects. In the first one, we analyze…

Optimization and Control · Mathematics 2018-05-16 Saeed Hadikhanloo , Francisco José Silva

Reinforcement learning has shown promise in learning policies that can solve complex problems. However, manually specifying a good reward function can be difficult, especially for intricate tasks. Inverse reinforcement learning offers a…

Machine Learning · Computer Science 2017-11-28 Peter Henderson , Wei-Di Chang , Pierre-Luc Bacon , David Meger , Joelle Pineau , Doina Precup

Entropy regularization has been extensively adopted to improve the efficiency, the stability, and the convergence of algorithms in reinforcement learning. This paper analyzes both quantitatively and qualitatively the impact of entropy…

Optimization and Control · Mathematics 2021-12-10 Xin Guo , Renyuan Xu , Thaleia Zariphopoulou

By following the study in [24], we consider an inverse boundary problem for the mean field game system where a probability density constraint is enforced on the game agents. That is, we consider the case that reflective boundary conditions…

Analysis of PDEs · Mathematics 2024-02-22 Hongyu Liu , Shen Zhang

Mean-field reinforcement learning has become a popular theoretical framework for efficiently approximating large-scale multi-agent reinforcement learning (MARL) problems exhibiting symmetry. However, questions remain regarding the…

Computer Science and Game Theory · Computer Science 2024-02-09 Batuhan Yardim , Artur Goldman , Niao He

Mean Field Game (MFG) models implicitly assume "rational expectations", meaning that the heterogeneous agents being modeled correctly know all relevant transition probabilities for the complex system they inhabit. When there is common…

Analysis of PDEs · Mathematics 2026-02-26 Benjamin Moll , Lenya Ryzhik

This paper introduces a new method based on Deep Galerkin Methods (DGMs) for solving high-dimensional stochastic Mean Field Games (MFGs). We achieve this by using two neural networks to approximate the unknown solutions of the MFG system…

Machine Learning · Computer Science 2023-08-09 Mouhcine Assouli , Badr Missaoui

Mean field games (MFG) are dynamic games with infinitely many infinitesimal agents. In this context, we study the efficiency of Nash MFG equilibria: Namely, we compare the social cost of a MFG equilibrium with the minimal cost a global…

Optimization and Control · Mathematics 2018-02-20 Pierre Cardaliaguet , Catherine Rainer