# Multi-Agent Inverse Reinforcement Learning for Identifying Pareto-Efficient Coordination -- A Distributionally Robust Approach

arXiv: https://arxiv.org/abs/2509.08956 · HTML: https://mlsanity.com/paper/2509.08956/

## 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 12 of its 58 references that are in the map.
- First posted on arXiv 10 Sep 2025.

## Placed in

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

## Builds on (most cited first, 12 of 12)

- [Maximum Entropy Deep Inverse Reinforcement Learning](https://mlsanity.com/paper/1507.04888/) (2015)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Multi-Objective Multi-Agent Decision Making: A Utility-based Analysis and Survey](https://mlsanity.com/paper/1909.02964/) (2019)
- [Identifying Cognitive Radars -- Inverse Reinforcement Learning using Revealed Preferences](https://mlsanity.com/paper/1912.00331/) (2019)
- [Meta-Cognition. An Inverse-Inverse Reinforcement Learning Approach for Cognitive Radars](https://mlsanity.com/paper/2205.01794/) (2022)
- [Wasserstein Distributionally Robust Look-Ahead Economic Dispatch](https://mlsanity.com/paper/2003.04874/) (2020)
- [Decomposition Algorithm for Distributionally Robust Optimization using Wasserstein Metric](https://mlsanity.com/paper/1704.03920/) (2017)
- [Wasserstein Distributionally Robust Inverse Multiobjective Optimization](https://mlsanity.com/paper/2009.14552/) (2020)
- [Identifying Coordination in a Cognitive Radar Network -- A Multi-Objective Inverse Reinforcement Learning Approach](https://mlsanity.com/paper/2211.06967/) (2022)
- [Energy and Age Pareto Optimal Trajectories in UAV-assisted Wireless Data Collection](https://mlsanity.com/paper/2106.03822/) (2021)
- [Statistical Detection of Coordination in a Cognitive Radar Network through Inverse Multi-objective Optimization](https://mlsanity.com/paper/2304.09125/) (2023)
- [UAV-Enabled Covert Wireless Data Collection](https://mlsanity.com/paper/1906.08438/) (2019)

## Abstract (arXiv)

Multi-agent inverse reinforcement learning (IRL) aims to identify Pareto-efficient behavior in a multi-agent system, and reconstruct utility functions of the individual agents. Motivated by the problem of detecting UAV coordination, how can we construct a statistical detector for Pareto-efficient behavior given noisy measurements of the decisions of a multi-agent system? This paper approaches this IRL problem by deriving necessary and sufficient conditions for a dataset of multi-agent system dynamics to be consistent with Pareto-efficient coordination, and providing algorithms for recovering utility functions which are consistent with the system dynamics. We derive an optimal statistical detector for determining Pareto-efficient coordination from noisy system measurements, which minimizes Type-I statistical detection error. Then, we provide a utility estimation algorithm which minimizes the worst-case estimation error over a statistical ambiguity set centered at empirical observations; this min-max solution achieves distributionally robust IRL, which is crucial in adversarial strategic interactions. We illustrate these results in a detailed example for detecting Pareto-efficient coordination among multiple UAVs given noisy measurement recorded at a radar. We then reconstruct the utility functions of the UAVs in a distributionally robust sense.