RL in Markov Games with Independent Function Approximation: Improved Sample Complexity Bound under the Local Access Model

Junyi Fan, Yuxuan Han, Jialin Zeng, Jian-Feng Cai, Yang Wang, Yang Xiang, Jiheng Zhang
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:2035-2043, 2024.

Abstract

Efficiently learning equilibria with large state and action spaces in general-sum Markov games while overcoming the curse of multi-agency is a challenging problem. Recent works have attempted to solve this problem by employing independent linear function classes to approximate the marginal $Q$-value for each agent. However, existing sample complexity bounds under such a framework have a suboptimal dependency on the desired accuracy $\varepsilon$ or the action space. In this work, we introduce a new algorithm, Lin-Confident-FTRL, for learning coarse correlated equilibria (CCE) with local access to the simulator, i.e., one can interact with the underlying environment on the visited states. Up to a logarithmic dependence on the size of the state space, Lin-Confident-FTRL learns $\epsilon$-CCE with a provable optimal accuracy bound $O(\epsilon^{-2})$ and gets rids of the linear dependency on the action space, while scaling polynomially with relevant problem parameters (such as the number of agents and time horizon). Moreover, our analysis of Linear-Confident-FTRL generalizes the virtual policy iteration technique in the single-agent local planning literature, which yields a new computationally efficient algorithm with a tighter sample complexity bound when assuming random access to the simulator.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-fan24b, title = {{RL} in {M}arkov Games with Independent Function Approximation: Improved Sample Complexity Bound under the Local Access Model}, author = {Fan, Junyi and Han, Yuxuan and Zeng, Jialin and Cai, Jian-Feng and Wang, Yang and Xiang, Yang and Zhang, Jiheng}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {2035--2043}, 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/fan24b/fan24b.pdf}, url = {https://proceedings.mlr.press/v238/fan24b.html}, abstract = {Efficiently learning equilibria with large state and action spaces in general-sum Markov games while overcoming the curse of multi-agency is a challenging problem. Recent works have attempted to solve this problem by employing independent linear function classes to approximate the marginal $Q$-value for each agent. However, existing sample complexity bounds under such a framework have a suboptimal dependency on the desired accuracy $\varepsilon$ or the action space. In this work, we introduce a new algorithm, Lin-Confident-FTRL, for learning coarse correlated equilibria (CCE) with local access to the simulator, i.e., one can interact with the underlying environment on the visited states. Up to a logarithmic dependence on the size of the state space, Lin-Confident-FTRL learns $\epsilon$-CCE with a provable optimal accuracy bound $O(\epsilon^{-2})$ and gets rids of the linear dependency on the action space, while scaling polynomially with relevant problem parameters (such as the number of agents and time horizon). Moreover, our analysis of Linear-Confident-FTRL generalizes the virtual policy iteration technique in the single-agent local planning literature, which yields a new computationally efficient algorithm with a tighter sample complexity bound when assuming random access to the simulator.} }
Endnote
%0 Conference Paper %T RL in Markov Games with Independent Function Approximation: Improved Sample Complexity Bound under the Local Access Model %A Junyi Fan %A Yuxuan Han %A Jialin Zeng %A Jian-Feng Cai %A Yang Wang %A Yang Xiang %A Jiheng Zhang %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-fan24b %I PMLR %P 2035--2043 %U https://proceedings.mlr.press/v238/fan24b.html %V 238 %X Efficiently learning equilibria with large state and action spaces in general-sum Markov games while overcoming the curse of multi-agency is a challenging problem. Recent works have attempted to solve this problem by employing independent linear function classes to approximate the marginal $Q$-value for each agent. However, existing sample complexity bounds under such a framework have a suboptimal dependency on the desired accuracy $\varepsilon$ or the action space. In this work, we introduce a new algorithm, Lin-Confident-FTRL, for learning coarse correlated equilibria (CCE) with local access to the simulator, i.e., one can interact with the underlying environment on the visited states. Up to a logarithmic dependence on the size of the state space, Lin-Confident-FTRL learns $\epsilon$-CCE with a provable optimal accuracy bound $O(\epsilon^{-2})$ and gets rids of the linear dependency on the action space, while scaling polynomially with relevant problem parameters (such as the number of agents and time horizon). Moreover, our analysis of Linear-Confident-FTRL generalizes the virtual policy iteration technique in the single-agent local planning literature, which yields a new computationally efficient algorithm with a tighter sample complexity bound when assuming random access to the simulator.
APA
Fan, J., Han, Y., Zeng, J., Cai, J., Wang, Y., Xiang, Y. & Zhang, J.. (2024). RL in Markov Games with Independent Function Approximation: Improved Sample Complexity Bound under the Local Access Model. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:2035-2043 Available from https://proceedings.mlr.press/v238/fan24b.html.

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