Mean field theory is decision making under uncertainty approach which responds to the agregate actions of many agents rather than agents individually.

## Our Papers on Mean Field Theory

Decentralized Mean Field Games

In

*Proceedings of the AAAI Conference on Artificial Intelligence (AAAI-2022)*.
Virtual.
Feb,
2022.

Multiagent reinforcement learning algorithms have not been widely adopted in large scale environments with many agents as they often scale poorly with the number of agents. Using mean field theory to aggregate agents has been proposed as a solution to this problem. However, almost all previous methods in this area make a strong assumption of a centralized system where all the agents in the environment learn the same policy and are effectively indistinguishable from each other. In this paper, we relax this assumption about indistinguishable agents and propose a new mean field system known as Decentralized Mean Field Games, where each agent can be quite different from others. All agents learn independent policies in a decentralized fashion, based on their local observations. We define a theoretical solution concept for this system and provide a fixed point guarantee for a Q-learning based algorithm in this system. A practical consequence of our approach is that we can address a ‘chicken-and-egg’ problem in empirical mean field reinforcement learning algorithms. Further, we provide Q-learning and actor-critic algorithms that use the decentralized mean field learning approach and give stronger performances compared to common baselines in this area. In our setting, agents do not need to be clones of each other and learn in a fully decentralized fashion. Hence, for the first time, we show the application of mean field learning methods in fully competitive environments, large-scale continuous action space environments, and other environments with heterogeneous agents. Importantly, we also apply the mean field method in a ride-sharing problem using a real-world dataset. We propose a decentralized solution to this problem, which is more practical than existing centralized training methods.

Partially Observable Mean Field Reinforcement Learning

In

*Proceedings of the 20th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS)*.
International Foundation for Autonomous Agents and Multiagent Systems,
London, United Kingdom.
May,
2021.

Traditional multi-agent reinforcement learning algorithms are not scalable to environments with more than a few agents, since these algorithms are exponential in the number of agents. Recent research has introduced successful methods to scale multi-agent reinforcement learning algorithms to many agent scenarios using mean field theory. Previous work in this field assumes that an agent has access to exact cumulative metrics regarding the mean field behaviour of the system, which it can then use to take its actions. In this paper, we relax this assumption and maintain a distribution to model the uncertainty regarding the mean field of the system. We consider two different settings for this problem. In the first setting, only agents in a fixed neighbourhood are visible, while in the second setting, the visibility of agents is determined at random based on distances. For each of these settings, we introduce a Q-learning based algorithm that can learn effectively. We prove that this Q-learning estimate stays very close to the Nash Q-value (under a common set of assumptions) for the first setting. We also empirically show our algorithms outperform multiple baselines in three different games in the MAgents framework, which supports large environments with many agents learning simultaneously to achieve possibly distinct goals.