Learning Equilibria from Data: Provably Efficient Multi-Agent Imitation Learning

• URL: http://arxiv.org/abs/2505.17610v1
• Date: Fri, 23 May 2025 08:18:35 GMT
• Title: Learning Equilibria from Data: Provably Efficient Multi-Agent Imitation Learning
• Authors: Till Freihaut, Luca Viano, Volkan Cevher, Matthieu Geist, Giorgia Ramponi,
• Abstract summary: We show that a new quantity named the single policy deviation concentrability coefficient is unavoidable in the non-interactive imitation learning setting.<n>We introduce two novel solution algorithms: MAIL-BRO and MURMAIL.<n>The latter bypasses completely the best response oracle at the cost of a worse expert query complexity of order $mathcalO(varepsilon-8)$.
• Score: 69.45910671974296
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper provides the first expert sample complexity characterization for learning a Nash equilibrium from expert data in Markov Games. We show that a new quantity named the single policy deviation concentrability coefficient is unavoidable in the non-interactive imitation learning setting, and we provide an upper bound for behavioral cloning (BC) featuring such coefficient. BC exhibits substantial regret in games with high concentrability coefficient, leading us to utilize expert queries to develop and introduce two novel solution algorithms: MAIL-BRO and MURMAIL. The former employs a best response oracle and learns an $\varepsilon$-Nash equilibrium with $\mathcal{O}(\varepsilon^{-4})$ expert and oracle queries. The latter bypasses completely the best response oracle at the cost of a worse expert query complexity of order $\mathcal{O}(\varepsilon^{-8})$. Finally, we provide numerical evidence, confirming our theoretical findings.

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