Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm

Fuzhong Zhou, Chenyu Zhang, Xu Chen, Xuan Di
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:62210-62256, 2024.

Abstract

We propose a discrete time graphon game formulation on continuous state and action spaces using a representative player to study stochastic games with heterogeneous interaction among agents. This formulation admits both conceptual and mathematical advantages, compared to a widely adopted formulation using a continuum of players. We prove the existence and uniqueness of the graphon equilibrium with mild assumptions, and show that this equilibrium can be used to construct an approximate solution for the finite player game, which is challenging to analyze and solve due to curse of dimensionality. An online oracle-free learning algorithm is developed to solve the equilibrium numerically, and sample complexity analysis is provided for its convergence.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-zhou24u, title = {Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm}, author = {Zhou, Fuzhong and Zhang, Chenyu and Chen, Xu and Di, Xuan}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {62210--62256}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/zhou24u/zhou24u.pdf}, url = {https://proceedings.mlr.press/v235/zhou24u.html}, abstract = {We propose a discrete time graphon game formulation on continuous state and action spaces using a representative player to study stochastic games with heterogeneous interaction among agents. This formulation admits both conceptual and mathematical advantages, compared to a widely adopted formulation using a continuum of players. We prove the existence and uniqueness of the graphon equilibrium with mild assumptions, and show that this equilibrium can be used to construct an approximate solution for the finite player game, which is challenging to analyze and solve due to curse of dimensionality. An online oracle-free learning algorithm is developed to solve the equilibrium numerically, and sample complexity analysis is provided for its convergence.} }
Endnote
%0 Conference Paper %T Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm %A Fuzhong Zhou %A Chenyu Zhang %A Xu Chen %A Xuan Di %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-zhou24u %I PMLR %P 62210--62256 %U https://proceedings.mlr.press/v235/zhou24u.html %V 235 %X We propose a discrete time graphon game formulation on continuous state and action spaces using a representative player to study stochastic games with heterogeneous interaction among agents. This formulation admits both conceptual and mathematical advantages, compared to a widely adopted formulation using a continuum of players. We prove the existence and uniqueness of the graphon equilibrium with mild assumptions, and show that this equilibrium can be used to construct an approximate solution for the finite player game, which is challenging to analyze and solve due to curse of dimensionality. An online oracle-free learning algorithm is developed to solve the equilibrium numerically, and sample complexity analysis is provided for its convergence.
APA
Zhou, F., Zhang, C., Chen, X. & Di, X.. (2024). Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:62210-62256 Available from https://proceedings.mlr.press/v235/zhou24u.html.

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