Mathieu Lauriere Papers

JMLR Journal 2025 Journal Article

Actor-Critic learning for mean-field control in continuous time

Noufel FRIKHA
Maximilien GERMAIN
Mathieu Lauriere
Huyen PHAM
Xuanye SONG

We study policy gradient for mean-field control in continuous time in a reinforcement learning setting. By considering randomised policies with entropy regularisation, we derive a gradient expectation representation of the value function, which is amenable to actor-critic type algorithms, where the value functions and the policies are learnt alternately based on observation samples of the state and model-free estimation of the population state distribution, either by offline or online learning. In the linear-quadratic mean-field framework, we obtain an exact parametrisation of the actor and critic functions defined on the Wasserstein space. Finally, we illustrate the results of our algorithms with some numerical experiments on concrete examples. [abs] [ pdf ][ bib ] &copy JMLR 2025. ( edit, beta )

PDF Details

RLJ Journal 2025 Journal Article

Reinforcement Learning for Finite Space Mean-Field Type Game

Kai Shao
Jiacheng Shen
Mathieu Lauriere

Mean field type games (MFTGs) describe Nash equilibria between large coalitions: each coalition consists of a continuum of cooperative agents who maximize the average reward of their coalition while interacting non-cooperatively with a finite number of other coalitions. Although the theory has been extensively developed, we are still lacking efficient and scalable computational methods. Here, we develop reinforcement learning methods for such games in a finite space setting with general dynamics and reward functions. We start by proving that MFTG solution yields approximate Nash equilibria in finite-size coalition games. We then propose two algorithms. The first is based on quantization of mean-field spaces and Nash Q-learning. We provide convergence and stability analysis. We then propose a deep reinforcement learning algorithm, which can scale to larger spaces. Numerical experiments in 4 environments with mean-field distributions of dimension up to $200$ show the scalability and efficiency of the proposed method.

PDF Details

RLC Conference 2025 Conference Paper

Reinforcement Learning for Finite Space Mean-Field Type Game

Kai Shao
Jiacheng Shen
Mathieu Lauriere

Mean field type games (MFTGs) describe Nash equilibria between large coalitions: each coalition consists of a continuum of cooperative agents who maximize the average reward of their coalition while interacting non-cooperatively with a finite number of other coalitions. Although the theory has been extensively developed, we are still lacking efficient and scalable computational methods. Here, we develop reinforcement learning methods for such games in a finite space setting with general dynamics and reward functions. We start by proving that MFTG solution yields approximate Nash equilibria in finite-size coalition games. We then propose two algorithms. The first is based on quantization of mean-field spaces and Nash Q-learning. We provide convergence and stability analysis. We then propose a deep reinforcement learning algorithm, which can scale to larger spaces. Numerical experiments in 4 environments with mean-field distributions of dimension up to $200$ show the scalability and efficiency of the proposed method.

PDF Details

NeurIPS Conference 2025 Conference Paper

Solving Continuous Mean Field Games: Deep Reinforcement Learning for Non-Stationary Dynamics

Lorenzo Magnino
Kai Shao
Zida Wu
Jiacheng Shen
Mathieu Lauriere

Mean field games (MFGs) have emerged as a powerful framework for modeling interactions in large-scale multi-agent systems. Despite recent advancements in reinforcement learning (RL) for MFGs, existing methods are typically limited to finite spaces or stationary models, hindering their applicability to real-world problems. This paper introduces a novel deep reinforcement learning (DRL) algorithm specifically designed for non-stationary continuous MFGs. The proposed approach builds upon a Fictitious Play (FP) methodology, leveraging DRL for best-response computation and supervised learning for average policy representation. Furthermore, it learns a representation of the time-dependent population distribution using a Conditional Normalizing Flow. To validate the effectiveness of our method, we evaluate it on three different examples of increasing complexity. By addressing critical limitations in scalability and density approximation, this work represents a significant advancement in applying DRL techniques to complex MFG problems, bringing the field closer to real-world multi-agent systems.

PDF Details

AAMAS Conference 2024 Conference Paper

Population-aware Online Mirror Descent for Mean-Field Games by Deep Reinforcement Learning

Zida Wu
Mathieu Lauriere
Samuel Jia Cong Chua
Matthieu Geist
Olivier Pietquin
Ankur Mehta

Mean Field Games (MFGs) have the ability to handle large-scale multi-agent systems, but learning Nash equilibria in MFGs remains a challenging task. In this paper, we propose a deep reinforcement learning (DRL) algorithm that achieves population-dependent Nash equilibrium without the need for averaging or sampling from history, inspired by Munchausen RL and Online Mirror Descent. Through the design of an additional inner-loop replay buffer, the agents can effectively learn to achieve Nash equilibrium from any distribution, mitigating catastrophic forgetting. The resulting policy can be applied to various initial distributions. Numerical experiments on four canonical examples demonstrate our algorithm has better convergence properties than SOTA algorithms, in particular a DRL version of Fictitious Play for population-dependent policies.

PDF

EWRL Workshop 2023 Workshop Paper

On Imitation in Mean-field Games

Giorgia Ramponi
Pavel Kolev
Olivier Pietquin
Niao He
Mathieu Lauriere
Matthieu Geist

We explore the problem of imitation learning (IL) in the context of mean-field games (MFGs), where the goal is to imitate the behavior of a population of agents following a Nash equilibrium policy according to some unknown payoff function. IL in MFGs presents new challenges compared to single-agent IL, particularly when both the reward function and the transition kernel depend on the population distribution. In this paper, departing from the existing literature on IL for MFGs, we introduce a new solution concept called the Nash imitation gap. Then we show that when only the reward depends on the population distribution, IL in MFGs can be reduced to single-agent IL with similar guarantees. However, when the dynamics is population-dependent, we provide a novel upper-bound that suggests IL is harder in this setting. To address this issue, we propose a new adversarial formulation where the reinforcement learning problem is replaced by a mean-field control (MFC) problem, suggesting progress in IL within MFGs may have to build upon MFC.

PDF

NeurIPS Conference 2023 Conference Paper

On Imitation in Mean-field Games

Giorgia Ramponi
Pavel Kolev
Olivier Pietquin
Niao He
Mathieu Lauriere
Matthieu Geist

We explore the problem of imitation learning (IL) in the context of mean-field games (MFGs), where the goal is to imitate the behavior of a population of agents following a Nash equilibrium policy according to some unknown payoff function. IL in MFGs presents new challenges compared to single-agent IL, particularly when both the reward function and the transition kernel depend on the population distribution. In this paper, departing from the existing literature on IL for MFGs, we introduce a new solution concept called the Nash imitation gap. Then we show that when only the reward depends on the population distribution, IL in MFGs can be reduced to single-agent IL with similar guarantees. However, when the dynamics is population-dependent, we provide a novel upper-bound that suggests IL is harder in this setting. To address this issue, we propose a new adversarial formulation where the reinforcement learning problem is replaced by a mean-field control (MFC) problem, suggesting progress in IL within MFGs may have to build upon MFC.

PDF Details

AAMAS Conference 2022 Conference Paper

Learning Equilibria in Mean-Field Games: Introducing Mean-Field PSRO

Paul Muller
Mark Rowland
Romuald Elie
Georgios Piliouras
Julien Perolat
Mathieu Lauriere
Raphael Marinier
Olivier Pietquin

Recent advances in multiagent learning have seen the introduction of a family of algorithms that revolve around the populationbased training method PSRO, showing convergence to Nash, correlated and coarse correlated equilibria. Notably, when the number of agents increases, learning best-responses becomes exponentially more difficult, and as such hampers PSRO training methods. The field of mean-field games provides an asymptotic solution to this problem when the considered games are anonymoussymmetric. Unfortunately, the mean-field approximation introduces non-linearities which prevent a straightforward adaptation of PSRO. Building upon optimization and adversarial regret minimization, this paper sidesteps this issue and introduces mean-field PSRO, an adaptation of PSRO which learns Nash, coarse correlated and correlated equilibria in mean-field games. The key is to replace the exact distribution computation step by newly-defined mean-field no-adversarial-regret learners, or by black-box optimization. We compare the asymptotic complexity of the approach to standard PSRO, greatly improve empirical bandit convergence speed by compressing temporal mixture weights, and ensure it is theoretically robust to payoff noise. Finally, we illustrate the speed and accuracy of mean-field PSRO on several mean-field games, demonstrating convergence to strong and weak equilibria.

PDF

EWRL Workshop 2022 Workshop Paper

Scalable Deep Reinforcement Learning Algorithms for Mean Field Games

Mathieu Lauriere
Sarah Perrin
Sertan Girgin
Paul Muller
Ayush Jain
Théophile Cabannes
Georgios Piliouras
Julien Perolat

Mean Field Games (MFGs) have been introduced to efficiently approximate games with very large populations of strategic agents. Recently, the question of learning equilibria in MFGs has gained momentum, particularly using model-free reinforcement learning (RL) methods. One limiting factor to further scale up using RL is that existing algorithms to solve MFGs require the mixing of approximated quantities such as strategies or q-values. This is non-trivial in the case of non-linear function approximation that enjoy good generalization properties, e.g. neural networks. We propose two methods to address this shortcoming. The first one learns a mixed strategy from distillation of historical data into a neural network and is applied to the Fictitious Play algorithm. The second one is an online mixing method based on regularization that does not require memorizing historical data or previous estimates. It is used to extend Online Mirror Descent. We demonstrate numerically that these methods efficiently enable the use of Deep RL algorithms to solve various MFGs. In addition, we show that these methods outperform SotA baselines from the literature.

PDF Details

NeurIPS Conference 2020 Conference Paper

Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications

Sarah Perrin
Julien Perolat
Mathieu Lauriere
Matthieu Geist
Romuald Elie
Olivier Pietquin

In this paper, we deepen the analysis of continuous time Fictitious Play learning algorithm to the consideration of various finite state Mean Field Game settings (finite horizon, $\gamma$-discounted), allowing in particular for the introduction of an additional common noise. We first present a theoretical convergence analysis of the continuous time Fictitious Play process and prove that the induced exploitability decreases at a rate $O(\frac{1}{t})$. Such analysis emphasizes the use of exploitability as a relevant metric for evaluating the convergence towards a Nash equilibrium in the context of Mean Field Games. These theoretical contributions are supported by numerical experiments provided in either model-based or model-free settings. We provide hereby for the first time converging learning dynamics for Mean Field Games in the presence of common noise.

PDF Details

Possible papers