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

Volkan Cevher (EPFL) · Luca Viano (EPFL) · Giorgia Ramponi (Department of Informatics, University of Zurich, University of Zurich) · Till Freihaut (Department of Informatics, University of Zurich) · Matthieu Geist (Earth Species Project)

$\varepsilon$-nash equilibriumbehavioral cloningbest response oracleexpert queriesexpert query complexitymail-bromarkov gamesmurmailnash equilibriumnon-interactive imitation learningnumerical evidenceregretsingle policy deviation concentrability coefficientsolution algorithmstheoretical findings

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.