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arXiv · 2510.09325

Rate optimal learning of equilibria from data

Till Freihaut·Luca Viano·Emanuele Nevali·Volkan Cevher·Matthieu Geist·Giorgia Ramponi
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Abstract

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 $\mathcal{O}(\varepsilon^{-8})$ to $\mathcal{O}(\varepsilon^{-2}),$ matching the dependence on $\varepsilon$ 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.

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Till Freihaut, Luca Viano, Emanuele Nevali, Volkan Cevher, Matthieu Geist, Giorgia Ramponi. 2025-10-10. Rate optimal learning of equilibria from data. https://arxiv.org/abs/2510.09325

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