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In this paper, we investigate the interaction of two populations with a large number of indistinguishable agents. The problem consists in two levels: the interaction between agents of a same population, and the interaction between the two…

Optimization and Control · Mathematics 2018-10-30 Alain Bensoussan , Tao Huang , Mathieu Laurière

Multi-agent reinforcement learning (MARL) addresses sequential decision-making problems with multiple agents, where each agent optimizes its own objective. In many real-world instances, the agents may not only want to optimize their…

Machine Learning · Computer Science 2023-06-14 Pragnya Alatur , Giorgia Ramponi , Niao He , Andreas Krause

One of the most critical aspects of multimodal Reinforcement Learning (RL) is the effective integration of different observation modalities. Having robust and accurate representations derived from these modalities is key to enhancing the…

Robotics · Computer Science 2024-06-21 Fotios Lygerakis , Vedant Dave , Elmar Rueckert

Reinforcement learning (RL) is increasingly applied to real-world problems involving complex and structured decisions, such as routing, scheduling, and assortment planning. These settings challenge standard RL algorithms, which struggle to…

Machine Learning · Computer Science 2025-10-29 Heiko Hoppe , Léo Baty , Louis Bouvier , Axel Parmentier , Maximilian Schiffer

We consider online reinforcement learning in Mean-Field Games (MFGs). Unlike traditional approaches, we alleviate the need for a mean-field oracle by developing an algorithm that approximates the Mean-Field Equilibrium (MFE) using the…

Machine Learning · Computer Science 2023-04-12 Muhammad Aneeq uz Zaman , Alec Koppel , Sujay Bhatt , Tamer Başar

Game-theoretic resource allocation on graphs (GRAG) involves two players competing over multiple steps to control nodes of interest on a graph, a problem modeled as a multi-step Colonel Blotto Game (MCBG). Finding optimal strategies is…

Machine Learning · Computer Science 2025-05-13 Zijian An , Lifeng Zhou

Continuous-time reinforcement learning (CTRL) provides a principled framework for sequential decision-making in environments where interactions evolve continuously over time. Despite its empirical success, the theoretical understanding of…

Machine Learning · Computer Science 2025-05-22 Runze Zhao , Yue Yu , Adams Yiyue Zhu , Chen Yang , Dongruo Zhou

Multi-agent reinforcement learning (MARL) optimizes strategic interactions in non-cooperative dynamic games, where agents have misaligned objectives. However, data-driven methods such as multi-agent policy gradients (MA-PG) often suffer…

Systems and Control · Electrical Eng. & Systems 2026-02-13 Jingqi Li , Gechen Qu , Jason J. Choi , Somayeh Sojoudi , Claire Tomlin

Counterfactual Regret Minimization (CRF) is a fundamental and effective technique for solving Imperfect Information Games (IIG). However, the original CRF algorithm only works for discrete state and action spaces, and the resulting strategy…

Artificial Intelligence · Computer Science 2018-12-31 Hui Li , Kailiang Hu , Zhibang Ge , Tao Jiang , Yuan Qi , Le Song

A central problem in the theory of multi-agent reinforcement learning (MARL) is to understand what structural conditions and algorithmic principles lead to sample-efficient learning guarantees, and how these considerations change as we move…

Machine Learning · Computer Science 2023-05-02 Dylan J. Foster , Dean P. Foster , Noah Golowich , Alexander Rakhlin

Traditional multi-agent reinforcement learning (MARL) algorithms, such as independent Q-learning, struggle when presented with partially observable scenarios, and where agents are required to develop delicate action sequences. This is often…

Machine Learning · Computer Science 2022-11-21 F. Bredell , H. A. Engelbrecht , J. C. Schoeman

The marriage between mean-field theory and reinforcement learning has shown a great capacity to solve large-scale control problems with homogeneous agents. To break the homogeneity restriction of mean-field theory, a recent interest is to…

Multiagent Systems · Computer Science 2026-03-03 Yuanquan Hu , Xiaoli Wei , Junji Yan , Hengxi Zhang

When controlling multi-agent systems, the trade-off between performance and scalability is a major challenge. Here, we address this difficulty by using mean field games (MFGs), which is a framework that deduces the macroscopic dynamics…

Optimization and Control · Mathematics 2021-08-06 Daisuke Inoue , Yuji Ito , Takahito Kashiwabara , Norikazu Saito , Hiroaki Yoshida

Cumulative entropy regularization introduces a regulatory signal to the reinforcement learning (RL) problem that encourages policies with high-entropy actions, which is equivalent to enforcing small deviations from a uniform reference…

Machine Learning · Computer Science 2019-09-16 Felix Leibfried , Jordi Grau-Moya

This paper proposes a novel Mean-Field Game (MFG) framework for large-scale attacker-defender systems aimed at protecting one or multiple High-Value Units (HVUs). Motivated by classical agent-wise attrition models, we introduce a…

Analysis of PDEs · Mathematics 2026-04-03 Avetik Arakelyan , Tigran Bakaryan , Davit Alaverdyan , Naira Hovakimyan , Isaac Kaminer

In this paper, we use mean field games (MFGs) to investigate approximations of $N$-player games with uniformly symmetrically continuous heterogeneous closed-loop actions. To incorporate agents' risk aversion (beyond the classical expected…

Optimization and Control · Mathematics 2024-09-26 Ziteng Cheng , Sebastian Jaimungal

Federated reinforcement learning (FRL) has emerged as a promising paradigm, enabling multiple agents to collaborate and learn a shared policy adaptable across heterogeneous environments. Among the various reinforcement learning (RL)…

Machine Learning · Computer Science 2024-12-25 Ye Zhu , Xiaowen Gong

While Reinforcement Learning ( RL) has made great strides towards solving increasingly complicated problems, many algorithms are still brittle to even slight environmental changes. Contextual Reinforcement Learning (cRL) provides a…

Financial markets and more generally macro-economic models involve a large number of individuals interacting through variables such as prices resulting from the aggregate behavior of all the agents. Mean field games have been introduced to…

Optimization and Control · Mathematics 2021-07-12 René Carmona , Mathieu Laurière

Mean field theory provides an effective way of scaling multiagent reinforcement learning algorithms to environments with many agents that can be abstracted by a virtual mean agent. In this paper, we extend mean field multiagent algorithms…

Multiagent Systems · Computer Science 2022-06-22 Sriram Ganapathi Subramanian , Pascal Poupart , Matthew E. Taylor , Nidhi Hegde