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In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…

Optimization and Control · Mathematics 2024-06-18 Gokce Dayanikli , Mathieu Lauriere

This work focuses on equilibrium selection in no-conflict multi-agent games, where we specifically study the problem of selecting a Pareto-optimal Nash equilibrium among several existing equilibria. It has been shown that many…

Machine Learning · Computer Science 2023-10-17 Filippos Christianos , Georgios Papoudakis , Stefano V. Albrecht

Markov Games (MG) is an important model for Multi-Agent Reinforcement Learning (MARL). It was long believed that the "curse of multi-agents" (i.e., the algorithmic performance drops exponentially with the number of agents) is unavoidable…

Machine Learning · Computer Science 2024-06-12 Yan Dai , Qiwen Cui , Simon S. Du

Multi-agent reinforcement learning (MARL) provides an efficient way for simultaneously learning policies for multiple agents interacting with each other. However, in scenarios requiring complex interactions, existing algorithms can suffer…

Machine Learning · Computer Science 2022-03-08 Xiaobai Ma , David Isele , Jayesh K. Gupta , Kikuo Fujimura , Mykel J. Kochenderfer

We study a new class of Markov games, \emph(multi-player) zero-sum Markov Games} with \emph{Networked separable interactions} (zero-sum NMGs), to model the local interaction structure in non-cooperative multi-agent sequential…

Computer Science and Game Theory · Computer Science 2025-07-15 Chanwoo Park , Kaiqing Zhang , Asuman Ozdaglar

Follow the regularized leader FTRL is the premier algorithm for online optimization. However, despite decades of research on its convergence in constrained optimization -- and potential games in particular -- its behavior remained hitherto…

Computer Science and Game Theory · Computer Science 2026-02-02 Ioannis Anagnostides , Ioannis Panageas , Nikolas Patris , Tuomas Sandholm

Offline reinforcement learning (RL) aims at learning an optimal strategy using a pre-collected dataset without further interactions with the environment. While various algorithms have been proposed for offline RL in the previous literature,…

Machine Learning · Computer Science 2023-03-02 Wei Xiong , Han Zhong , Chengshuai Shi , Cong Shen , Liwei Wang , Tong Zhang

Provably efficient and robust equilibrium computation in general-sum Markov games remains a core challenge in multi-agent reinforcement learning. Nash equilibrium is computationally intractable in general and brittle due to equilibrium…

Machine Learning · Computer Science 2026-03-11 Jake Gonzales , Max Horwitz , Eric Mazumdar , Lillian J. Ratliff

Meta reinforcement learning (meta RL), as a combination of meta-learning ideas and reinforcement learning (RL), enables the agent to adapt to different tasks using a few samples. However, this sampling-based adaptation also makes meta RL…

Machine Learning · Computer Science 2023-03-09 Tao Li , Haozhe Lei , Quanyan Zhu

Existing studies on provably efficient algorithms for Markov games (MGs) almost exclusively build on the "optimism in the face of uncertainty" (OFU) principle. This work focuses on a different approach of posterior sampling, which is…

Machine Learning · Computer Science 2022-10-06 Wei Xiong , Han Zhong , Chengshuai Shi , Cong Shen , Tong Zhang

Multi-agent reinforcement learning (MARL), as a thriving field, explores how multiple agents independently make decisions in a shared dynamic environment. Due to environmental uncertainties, policies in MARL must remain robust to tackle the…

Machine Learning · Computer Science 2025-12-02 Na Li , Zewu Zheng , Wei Ni , Hangguan Shan , Wenjie Zhang , Xinyu Li

This paper addresses the problem of multi-agent inverse reinforcement learning (MIRL) in a two-player general-sum stochastic game framework. Five variants of MIRL are considered: uCS-MIRL, advE-MIRL, cooE-MIRL, uCE-MIRL, and uNE-MIRL, each…

Machine Learning · Computer Science 2021-01-01 Xiaomin Lin , Stephen C. Adams , Peter A. Beling

We motivate and propose a new model for non-cooperative Markov game which considers the interactions of risk-aware players. This model characterizes the time-consistent dynamic "risk" from both stochastic state transitions (inherent to the…

Computer Science and Game Theory · Computer Science 2019-11-22 Wenjie Huang , Pham Viet Hai , William B. Haskell

We present a method enabling a large number of agents to learn how to flock, which is a natural behavior observed in large populations of animals. This problem has drawn a lot of interest but requires many structural assumptions and is…

Multiagent Systems · Computer Science 2021-05-18 Sarah Perrin , Mathieu Laurière , Julien Pérolat , Matthieu Geist , Romuald Élie , Olivier Pietquin

We consider a multi-agent Markov strategic interaction over an infinite horizon where agents can be of multiple types. We model the strategic interaction as a mean-field game in the asymptotic limit when the number of agents of each type…

Multiagent Systems · Computer Science 2021-01-01 Arnob Ghosh , Vaneet Aggarwal

In cellular networks, User Equipment (UE) handoff from one Base Station (BS) to another, giving rise to the load balancing problem among the BSs. To address this problem, BSs can work collaboratively to deliver a smooth migration (or…

Artificial Intelligence · Computer Science 2023-03-15 Jikun Kang , Di Wu , Ju Wang , Ekram Hossain , Xue Liu , Gregory Dudek

The focus of this paper is a Bayesian framework for solving a class of problems termed multi-agent inverse reinforcement learning (MIRL). Compared to the well-known inverse reinforcement learning (IRL) problem, MIRL is formalized in the…

Computer Science and Game Theory · Computer Science 2019-07-31 Xiaomin Lin , Peter A. Beling , Randy Cogill

We study distributionally robust Markov games (DR-MGs) with the average-reward criterion, a framework for multi-agent decision-making under uncertainty over extended horizons. In average reward DR-MGs, agents aim to maximize their…

Multiagent Systems · Computer Science 2025-12-12 Zachary Roch , Yue Wang

We propose the concept of a Lagrangian game to solve constrained Markov games. Such games model scenarios where agents face cost constraints in addition to their individual rewards, that depend on both agent joint actions and the evolving…

Optimization and Control · Mathematics 2025-03-14 Soham Das , Santiago Paternain , Luiz F. O. Chamon , Ceyhun Eksin

We introduce and study a two-player zero-sum game between a probabilist and Nature defined by a convex function $f$, a finite collection $\mathcal{B}$ of Markov generators (or its convex hull), and a target distribution $\pi$. The…

Probability · Mathematics 2025-09-11 Michael C. H. Choi , Geoffrey Wolfer