# Multi-Agent Imitation Learning with Copulas

arXiv: https://arxiv.org/abs/2107.04750 · HTML: https://mlsanity.com/paper/2107.04750/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 18 of its 37 references that are in the map.
- First posted on arXiv 10 Jul 2021.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 18 of 18)

- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Learning Robust Rewards with Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1710.11248/) (2017)
- [Learning Multiagent Communication with Backpropagation](https://mlsanity.com/paper/1605.07736/) (2016)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Multi-Agent Deep Reinforcement Learning for Large-scale Traffic Signal Control](https://mlsanity.com/paper/1903.04527/) (2019)
- [Autonomous Agents Modelling Other Agents: A Comprehensive Survey and Open Problems](https://mlsanity.com/paper/1709.08071/) (2017)
- [Multi-Agent Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1807.09936/) (2018)
- [Coordinated Multi-Agent Imitation Learning](https://mlsanity.com/paper/1703.03121/) (2017)
- [Multi-Agent Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1907.13220/) (2019)
- [VAIN: Attentional Multi-agent Predictive Modeling](https://mlsanity.com/paper/1706.06122/) (2017)
- [Multi-Agent Imitation Learning for Driving Simulation](https://mlsanity.com/paper/1803.01044/) (2018)
- [Generating Multi-Agent Trajectories using Programmatic Weak Supervision](https://mlsanity.com/paper/1803.07612/) (2018)
- [Generative Modeling of Multimodal Multi-Human Behavior](https://mlsanity.com/paper/1803.02015/) (2018)
- [Multi-Agent Interactions Modeling with Correlated Policies](https://mlsanity.com/paper/2001.03415/) (2020)
- [A Regularized Opponent Model with Maximum Entropy Objective](https://mlsanity.com/paper/1905.08087/) (2019)
- [RoboCupSimData: A RoboCup soccer research dataset](https://mlsanity.com/paper/1711.01703/) (2017)

## Built on by (most cited first, 13 of 13)

- [Implicit Generative Copulas](https://mlsanity.com/paper/2109.14567/) (2021)
- [MAPF-GPT: Imitation Learning for Multi-Agent Pathfinding at Scale](https://mlsanity.com/paper/2409.00134/) (2024)
- [Copula Density Neural Estimation](https://mlsanity.com/paper/2211.15353/) (2022)
- [Adaptive action supervision in reinforcement learning from real-world multi-agent demonstrations](https://mlsanity.com/paper/2305.13030/) (2023)
- [Your copula is a classifier in disguise: classification-based copula density estimation](https://mlsanity.com/paper/2411.03014/) (2024)
- [Diffusion and Flow-based Copulas: Forgetting and Remembering Dependencies](https://mlsanity.com/paper/2509.19707/) (2025)
- [Inference and Sampling for Archimax Copulas](https://mlsanity.com/paper/2205.14025/) (2022)
- [DM2: Decentralized Multi-Agent Reinforcement Learning for Distribution Matching](https://mlsanity.com/paper/2206.00233/) (2022)
- [Advancing Learnable Multi-Agent Pathfinding Solvers with Active Fine-Tuning](https://mlsanity.com/paper/2506.23793/) (2025)
- [The Multi-Agent Pickup and Delivery Problem: MAPF, MARL and Its Warehouse Applications](https://mlsanity.com/paper/2203.07092/) (2022)
- [Enabling Multi-Robot Collaboration from Single-Human Guidance](https://mlsanity.com/paper/2409.19831/) (2024)
- [Matching Multiple Experts: On the Exploitability of Multi-Agent Imitation Learning](https://mlsanity.com/paper/2602.21020/) (2026)
- [MARL-GPT: Foundation Model for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2604.05943/) (2026)

## Abstract (arXiv)

Multi-agent imitation learning aims to train multiple agents to perform tasks from demonstrations by learning a mapping between observations and actions, which is essential for understanding physical, social, and team-play systems. However, most existing works on modeling multi-agent interactions typically assume that agents make independent decisions based on their observations, ignoring the complex dependence among agents. In this paper, we propose to use copula, a powerful statistical tool for capturing dependence among random variables, to explicitly model the correlation and coordination in multi-agent systems. Our proposed model is able to separately learn marginals that capture the local behavioral patterns of each individual agent, as well as a copula function that solely and fully captures the dependence structure among agents. Extensive experiments on synthetic and real-world datasets show that our model outperforms state-of-the-art baselines across various scenarios in the action prediction task, and is able to generate new trajectories close to expert demonstrations.