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We study policy optimization in Stackelberg mean field games (MFGs), a hierarchical framework for modeling the strategic interaction between a single leader and an infinitely large population of homogeneous followers. The objective can be…

Machine Learning · Computer Science 2025-11-27 Sihan Zeng , Benjamin Patrick Evans , Sujay Bhatt , Leo Ardon , Sumitra Ganesh , Alec Koppel

Multi-agent deep reinforcement learning has been applied to address a variety of complex problems with either discrete or continuous action spaces and achieved great success. However, most real-world environments cannot be described by only…

Machine Learning · Computer Science 2022-06-13 Hongzhi Hua , Kaigui Wu , Guixuan Wen

Deep reinforcement learning (DRL) has become a powerful tool for complex decision-making in machine learning and AI. However, traditional methods often assume perfect action execution, overlooking the uncertainties and deviations between an…

Robotics · Computer Science 2025-07-02 Oren Fivel , Matan Rudman , Kobi Cohen

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…

Computer Science and Game Theory · Computer Science 2024-03-07 Zida Wu , Mathieu Lauriere , Samuel Jia Cong Chua , Matthieu Geist , Olivier Pietquin , Ankur Mehta

We propose a mean field game (MFG) framework to model the evolution of renewable energy production in competitive electricity markets. Producers interact through the spot price while optimising their profits under production, installation,…

Optimization and Control · Mathematics 2026-03-25 Luciano Campi , Zhuoshu Wu

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

We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium -- such as Nash equilibrium and (Coarse) Correlated Equilibrium -- from an offline dataset pre-collected from…

Machine Learning · Computer Science 2023-02-07 Yuheng Zhang , Yu Bai , Nan Jiang

In this paper, we investigate a class of Mean Field Games (MFGs) in which the state dynamics are governed by multidimensional reflected stochastic differential equations (SDEs). We establish the existence of an equilibrium and show that it…

Probability · Mathematics 2026-03-17 Ayoub Laayoun , Badr Missaoui

Many applications, e.g., in shared mobility, require coordinating a large number of agents. Mean-field reinforcement learning addresses the resulting scalability challenge by optimizing the policy of a representative agent interacting with…

Machine Learning · Computer Science 2023-12-29 Matej Jusup , Barna Pásztor , Tadeusz Janik , Kenan Zhang , Francesco Corman , Andreas Krause , Ilija Bogunovic

Deploying controllers trained with Reinforcement Learning (RL) on real robots can be challenging: RL relies on agents' policies being modeled as Markov Decision Processes (MDPs), which assume an inherently discrete passage of time. The use…

Robotics · Computer Science 2024-04-03 Dong Wang , Giovanni Beltrame

Deep Reinforcement Learning (DRL) has been applied to address a variety of cooperative multi-agent problems with either discrete action spaces or continuous action spaces. However, to the best of our knowledge, no previous work has ever…

Machine Learning · Computer Science 2019-06-04 Haotian Fu , Hongyao Tang , Jianye Hao , Zihan Lei , Yingfeng Chen , Changjie Fan

We propose the Mean-Field Actor-Critic (MFAC) flow, a continuous-time learning dynamics for solving mean-field games (MFGs), combining techniques from reinforcement learning and optimal transport. The MFAC framework jointly evolves the…

Optimization and Control · Mathematics 2025-10-27 Mo Zhou , Haosheng Zhou , Ruimeng Hu

Mean Field Games (MFGs) can potentially scale multi-agent systems to extremely large populations of agents. Yet, most of the literature assumes a single initial distribution for the agents, which limits the practical applications of MFGs.…

Machine Learning · Computer Science 2021-09-21 Sarah Perrin , Mathieu Laurière , Julien Pérolat , Romuald Élie , Matthieu Geist , Olivier Pietquin

Reinforcement Learning (RL) is a learning paradigm concerned with learning to control a system so as to maximize an objective over the long term. This approach to learning has received immense interest in recent times and success manifests…

Artificial Intelligence · Computer Science 2018-07-26 Sanyam Kapoor

Modern reinforcement learning (RL) commonly engages practical problems with large state spaces, where function approximation must be deployed to approximate either the value function or the policy. While recent progresses in RL theory…

Machine Learning · Computer Science 2021-10-14 Chi Jin , Qinghua Liu , Tiancheng Yu

In this paper, we explore using deep reinforcement learning for problems with multiple agents. Most existing methods for deep multi-agent reinforcement learning consider only a small number of agents. When the number of agents increases,…

Machine Learning · Computer Science 2018-05-24 Arbaaz Khan , Clark Zhang , Daniel D. Lee , Vijay Kumar , Alejandro Ribeiro

We study the sample complexity of reinforcement learning (RL) in Mean-Field Games (MFGs) with model-based function approximation that requires strategic exploration to find a Nash Equilibrium policy. We introduce the Partial Model-Based…

Machine Learning · Computer Science 2024-06-04 Jiawei Huang , Niao He , Andreas Krause

Multi-agent reinforcement learning, despite its popularity and empirical success, faces significant scalability challenges in large-population dynamic games. Graphon mean field games (GMFGs) offer a principled framework for approximating…

Optimization and Control · Mathematics 2025-06-09 Philipp Plank , Yufei Zhang

Designing socially optimal policies in multi-agent environments is a fundamental challenge in both economics and artificial intelligence. This paper studies a general framework for learning Stackelberg equilibria in dynamic and uncertain…

Systems and Control · Electrical Eng. & Systems 2025-09-23 Jun He , Andrew L. Liu , Yihsu Chen

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
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