We close open theoretical gaps in Multi-Agent Imitation Learning (MAIL) by characterizing the limits of non-interactive MAIL and presenting the first interactive algorithm with near-optimal sample complexity. In the non-interactive setting, we prove a statistical lower bound that identifies the all-policy deviation concentrability coefficient as the fundamental complexity measure, and we show that Behavior Cloning (BC) is rate-optimal. For the interactive setting, we introduce a framework that combines reward-free reinforcement learning with interactive MAIL and instantiate it with an algorithm, MAIL-WARM. It improves the best previously known sample complexity from O(ε−8) to O(ε−2), matching the dependence on ε implied by our lower bound. Finally, we provide numerical results that support our theory and illustrate, in environments such as grid worlds, where Behavior Cloning fails to learn.
@article{arxiv.2510.09325,
title = {Rate optimal learning of equilibria from data},
author = {Till Freihaut and Luca Viano and Emanuele Nevali and Volkan Cevher and Matthieu Geist and Giorgia Ramponi},
journal= {arXiv preprint arXiv:2510.09325},
year = {2025}
}