Finite-sample guarantees for Nash Q-learning with linear function approximation
Pedro Cisneros-Velarde, Sanmi Koyejo
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.
BibTeX
@InProceedings{pmlr-v216-cisneros-velarde23a,
title = {Finite-sample guarantees for {N}ash {Q}-learning with linear function approximation},
author = {Cisneros-Velarde, Pedro and Koyejo, Sanmi},
booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence},
pages = {424--432},
year = {2023},
editor = {Evans, Robin J. and Shpitser, Ilya},
volume = {216},
series = {Proceedings of Machine Learning Research},
month = {31 Jul--04 Aug},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v216/cisneros-velarde23a/cisneros-velarde23a.pdf},
url = {https://proceedings.mlr.press/v216/cisneros-velarde23a.html},
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.}
}