---
title: "Mean Field Games Flock! The Reinforcement Learning Way"
authors:
  - "Sarah Perrin"
  - "Mathieu Laurière"
  - "Julien Pérolat"
  - "Matthieu Geist"
  - "Romuald Élie"
  - "Olivier Pietquin"
doi: "10.24963/ijcai.2021/50"
url: "https://ijcai.org/proceedings/2021/50"
pdf: "https://ijcai.org/proceedings/2021/0050.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "356-362"
track: "Main Track"
keywords:
  - "Agent-based and Multi-agent Systems: Noncooperative Games"
  - "Machine Learning Applications: Applications of Reinforcement Learning"
  - "Agent-based and Multi-agent Systems: Multi-agent Learning"
---

# Mean Field Games Flock! The Reinforcement Learning Way

Sarah Perrin, Mathieu Laurière, Julien Pérolat, Matthieu Geist, Romuald Élie, Olivier Pietquin

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 356-362. DOI: [10.24963/ijcai.2021/50](https://doi.org/10.24963/ijcai.2021/50)

## Abstract

We present a method enabling a large number of agents to learn how to flock. This problem has drawn a lot of interest but requires many structural assumptions and is tractable only in small dimensions. We phrase this problem as a Mean Field Game (MFG),  where each individual chooses its own acceleration depending on the population behavior. Combining Deep Reinforcement Learning (RL) and Normalizing Flows (NF), we obtain a tractable solution requiring only very weak assumptions. Our algorithm finds a Nash Equilibrium and the agents adapt their velocity to match the neighboring flock’s average one. We use Fictitious Play and alternate: (1) computing an approximate best response with Deep RL, and (2) estimating the next population distribution with NF. We show numerically that our algorithm can learn multi-group or high-dimensional flocking with obstacles.