# Mean Field Correlated Imitation Learning

arXiv: https://arxiv.org/abs/2404.09324 · HTML: https://mlsanity.com/paper/2404.09324/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse reinforcement learning, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 14 Apr 2024.

## Placed in

- Offline RL and imitation learning from data / [Inverse reinforcement learning](https://mlsanity.com/offlinerl/inverse-reinforcement-learning/)

## Builds on (most cited first, 13 of 13)

- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Mean Field Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1802.05438/) (2018)
- [Multi-Agent Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1807.09936/) (2018)
- [Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learning](https://mlsanity.com/paper/2102.01585/) (2021)
- [Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications](https://mlsanity.com/paper/2007.03458/) (2020)
- [Learning in Mean Field Games: A Survey](https://mlsanity.com/paper/2205.12944/) (2022)
- [Multi-Agent Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1907.13220/) (2019)
- [Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU](https://mlsanity.com/paper/2001.00706/) (2020)
- [Mean Field Games Flock! The Reinforcement Learning Way](https://mlsanity.com/paper/2105.07933/) (2021)
- [Computational Rationalization: The Inverse Equilibrium Problem](https://mlsanity.com/paper/1308.3506/) (2013)
- [Learning Equilibria in Mean-Field Games: Introducing Mean-Field PSRO](https://mlsanity.com/paper/2111.08350/) (2021)
- [Adversarial Inverse Reinforcement Learning for Mean Field Games](https://mlsanity.com/paper/2104.14654/) (2021)
- [Correlated equilibria and mean field games: a simple model](https://mlsanity.com/paper/2004.06185/) (2020)

## Abstract (arXiv)

We investigate multi-agent imitation learning (IL) within the framework of mean field games (MFGs), considering the presence of time-varying correlated signals. Existing MFG IL algorithms assume demonstrations are sampled from Mean Field Nash Equilibria (MFNE), limiting their adaptability to real-world scenarios. For example, in the traffic network equilibrium influenced by public routing recommendations, recommendations introduce time-varying correlated signals into the game, not captured by MFNE and other existing correlated equilibrium concepts. To address this gap, we propose Adaptive Mean Field Correlated Equilibrium (AMFCE), a general equilibrium incorporating time-varying correlated signals. We establish the existence of AMFCE under mild conditions and prove that MFNE is a subclass of AMFCE. We further propose Correlated Mean Field Imitation Learning (CMFIL), a novel IL framework designed to recover the AMFCE, accompanied by a theoretical guarantee on the quality of the recovered policy. Experimental results, including a real-world traffic flow prediction problem, demonstrate the superiority of CMFIL over state-of-the-art IL baselines, highlighting the potential of CMFIL in understanding large population behavior under correlated signals.