Lorenzo Magnino

Lorenzo Magnino, Jiacheng Shen, Matthieu Geist et al.

The intersection of Mean Field Games (MFGs) and Reinforcement Learning (RL) has fostered a growing family of algorithms designed to solve large-scale multi-agent systems. However, the field currently lacks a standardized evaluation protocol, forcing researchers to rely on bespoke, isolated, and often simplistic environments. This fragmentation makes it difficult to assess the robustness, generalization, and failure modes of emerging methods. To address this gap, we propose a comprehensive benchmark suite for MFGs (Bench-MFG), focusing on the discrete-time, discrete-space, stationary setting for the sake of clarity. We introduce a taxonomy of problem classes, ranging from no-interaction and monotone games to potential and dynamics-coupled games, and provide prototypical environments for each. Furthermore, we propose MF-Garnets, a method for generating random MFG instances to facilitate rigorous statistical testing. We benchmark a variety of learning algorithms across these environments, including a novel black-box approach (MF-PSO) for exploitability minimization. Based on our extensive empirical results, we propose guidelines to standardize future experimental comparisons. Code available at \href{https://github.com/lorenzomagnino/Bench-MFG}{https://github.com/lorenzomagnino/Bench-MFG}.

Lorenzo Magnino, Yuchen Zhu, Mathieu Laurière

Optimal stopping is a fundamental problem in optimization with applications in risk management, finance, robotics, and machine learning. We extend the standard framework to a multi-agent setting, named multi-agent optimal stopping (MAOS), where agents cooperate to make optimal stopping decisions in a finite-space, discrete-time environment. Since solving MAOS becomes computationally prohibitive as the number of agents is very large, we study the mean-field optimal stopping (MFOS) problem, obtained as the number of agents tends to infinity. We establish that MFOS provides a good approximation to MAOS and prove a dynamic programming principle (DPP) based on mean-field control theory. We then propose two deep learning approaches: one that learns optimal stopping decisions by simulating full trajectories and another that leverages the DPP to compute the value function and to learn the optimal stopping rule using backward induction. Both methods train neural networks to approximate optimal stopping policies. We demonstrate the effectiveness and the scalability of our work through numerical experiments on 6 different problems in spatial dimension up to 300. To the best of our knowledge, this is the first work to formalize and computationally solve MFOS in discrete time and finite space, opening new directions for scalable MAOS methods.