On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximation

Jiawei Huang, Batuhan Yardim, Niao He
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:289-297, 2024.

Abstract

In this paper, we study the fundamental statistical efficiency of Reinforcement Learning in Mean-Field Control (MFC) and Mean-Field Game (MFG) with general model-based function approximation. We introduce a new concept called Mean-Field Model-Based Eluder Dimension (MF-MBED), which characterizes the inherent complexity of mean-field model classes. We show that a rich family of Mean-Field RL problems exhibits low MF-MBED. Additionally, we propose algorithms based on maximal likelihood estimation, which can return an $\epsilon$-optimal policy for MFC or an $\epsilon$-Nash Equilibrium policy for MFG. The overall sample complexity depends only polynomially on MF-MBED, which is potentially much lower than the size of state-action space. Compared with previous works, our results only require the minimal assumptions including realizability and Lipschitz continuity.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-huang24a, title = {On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximation}, author = {Huang, Jiawei and Yardim, Batuhan and He, Niao}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {289--297}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/huang24a/huang24a.pdf}, url = {https://proceedings.mlr.press/v238/huang24a.html}, abstract = {In this paper, we study the fundamental statistical efficiency of Reinforcement Learning in Mean-Field Control (MFC) and Mean-Field Game (MFG) with general model-based function approximation. We introduce a new concept called Mean-Field Model-Based Eluder Dimension (MF-MBED), which characterizes the inherent complexity of mean-field model classes. We show that a rich family of Mean-Field RL problems exhibits low MF-MBED. Additionally, we propose algorithms based on maximal likelihood estimation, which can return an $\epsilon$-optimal policy for MFC or an $\epsilon$-Nash Equilibrium policy for MFG. The overall sample complexity depends only polynomially on MF-MBED, which is potentially much lower than the size of state-action space. Compared with previous works, our results only require the minimal assumptions including realizability and Lipschitz continuity.} }
Endnote
%0 Conference Paper %T On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximation %A Jiawei Huang %A Batuhan Yardim %A Niao He %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-huang24a %I PMLR %P 289--297 %U https://proceedings.mlr.press/v238/huang24a.html %V 238 %X In this paper, we study the fundamental statistical efficiency of Reinforcement Learning in Mean-Field Control (MFC) and Mean-Field Game (MFG) with general model-based function approximation. We introduce a new concept called Mean-Field Model-Based Eluder Dimension (MF-MBED), which characterizes the inherent complexity of mean-field model classes. We show that a rich family of Mean-Field RL problems exhibits low MF-MBED. Additionally, we propose algorithms based on maximal likelihood estimation, which can return an $\epsilon$-optimal policy for MFC or an $\epsilon$-Nash Equilibrium policy for MFG. The overall sample complexity depends only polynomially on MF-MBED, which is potentially much lower than the size of state-action space. Compared with previous works, our results only require the minimal assumptions including realizability and Lipschitz continuity.
APA
Huang, J., Yardim, B. & He, N.. (2024). On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximation. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:289-297 Available from https://proceedings.mlr.press/v238/huang24a.html.

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