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# Finite-sample guarantees for Nash Q-learning with linear function approximation

*Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence*, PMLR 216:424-432, 2023.

#### Abstract

Nash Q-learning may be considered one of the first and most known algorithms in multi-agent reinforcement learning (MARL) for learning policies that constitute a Nash equilibrium of an underlying general-sum Markov game. Its original proof provided asymptotic guarantees and was for the tabular case. Recently, finite-sample guarantees have been provided using more modern RL techniques for the tabular case. Our work analyzes Nash Q-learning using linear function approximation – a representation regime introduced when the state space is large or continuous – and provides finite-sample guarantees that indicate its sample efficiency. We find that the obtained performance nearly matches an existing efficient result for single-agent RL under the same representation and has a polynomial gap when compared to the best-known result for the tabular case.