Finite-sample Guarantees for Nash Q-learning with Linear Function Approximation
This work addresses the sample efficiency challenge for multi-agent reinforcement learning in large or continuous state spaces, representing an incremental advance by extending finite-sample guarantees to linear function approximation.
The paper tackles the problem of providing finite-sample guarantees for Nash Q-learning with linear function approximation in multi-agent reinforcement learning, showing that its sample efficiency nearly matches single-agent RL results and has a polynomial gap compared to tabular cases.
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.