A Sharp Analysis of Model-based Reinforcement Learning with Self-Play

Qinghua Liu, Tiancheng Yu, Yu Bai, Chi Jin
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:7001-7010, 2021.

Abstract

Model-based algorithms—algorithms that explore the environment through building and utilizing an estimated model—are widely used in reinforcement learning practice and theoretically shown to achieve optimal sample efficiency for single-agent reinforcement learning in Markov Decision Processes (MDPs). However, for multi-agent reinforcement learning in Markov games, the current best known sample complexity for model-based algorithms is rather suboptimal and compares unfavorably against recent model-free approaches. In this paper, we present a sharp analysis of model-based self-play algorithms for multi-agent Markov games. We design an algorithm \emph{Optimistic Nash Value Iteration} (Nash-VI) for two-player zero-sum Markov games that is able to output an ϵ-approximate Nash policy in ˜O(H3SAB/ϵ2) episodes of game playing, where S is the number of states, A,B are the number of actions for the two players respectively, and H is the horizon length. This significantly improves over the best known model-based guarantee of ˜O(H4S2AB/ϵ2), and is the first that matches the information-theoretic lower bound Ω(H3S(A+B)/ϵ2) except for a min factor. In addition, our guarantee compares favorably against the best known model-free algorithm if \min\{A,B\}=o(H^3), and outputs a single Markov policy while existing sample-efficient model-free algorithms output a nested mixture of Markov policies that is in general non-Markov and rather inconvenient to store and execute. We further adapt our analysis to designing a provably efficient task-agnostic algorithm for zero-sum Markov games, and designing the first line of provably sample-efficient algorithms for multi-player general-sum Markov games.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-liu21z, title = {A Sharp Analysis of Model-based Reinforcement Learning with Self-Play}, author = {Liu, Qinghua and Yu, Tiancheng and Bai, Yu and Jin, Chi}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {7001--7010}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/liu21z/liu21z.pdf}, url = {https://proceedings.mlr.press/v139/liu21z.html}, abstract = {Model-based algorithms—algorithms that explore the environment through building and utilizing an estimated model—are widely used in reinforcement learning practice and theoretically shown to achieve optimal sample efficiency for single-agent reinforcement learning in Markov Decision Processes (MDPs). However, for multi-agent reinforcement learning in Markov games, the current best known sample complexity for model-based algorithms is rather suboptimal and compares unfavorably against recent model-free approaches. In this paper, we present a sharp analysis of model-based self-play algorithms for multi-agent Markov games. We design an algorithm \emph{Optimistic Nash Value Iteration} (Nash-VI) for two-player zero-sum Markov games that is able to output an $\epsilon$-approximate Nash policy in $\tilde{\mathcal{O}}(H^3SAB/\epsilon^2)$ episodes of game playing, where $S$ is the number of states, $A,B$ are the number of actions for the two players respectively, and $H$ is the horizon length. This significantly improves over the best known model-based guarantee of $\tilde{\mathcal{O}}(H^4S^2AB/\epsilon^2)$, and is the first that matches the information-theoretic lower bound $\Omega(H^3S(A+B)/\epsilon^2)$ except for a $\min\{A,B\}$ factor. In addition, our guarantee compares favorably against the best known model-free algorithm if $\min\{A,B\}=o(H^3)$, and outputs a single Markov policy while existing sample-efficient model-free algorithms output a nested mixture of Markov policies that is in general non-Markov and rather inconvenient to store and execute. We further adapt our analysis to designing a provably efficient task-agnostic algorithm for zero-sum Markov games, and designing the first line of provably sample-efficient algorithms for multi-player general-sum Markov games.} }
Endnote
%0 Conference Paper %T A Sharp Analysis of Model-based Reinforcement Learning with Self-Play %A Qinghua Liu %A Tiancheng Yu %A Yu Bai %A Chi Jin %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-liu21z %I PMLR %P 7001--7010 %U https://proceedings.mlr.press/v139/liu21z.html %V 139 %X Model-based algorithms—algorithms that explore the environment through building and utilizing an estimated model—are widely used in reinforcement learning practice and theoretically shown to achieve optimal sample efficiency for single-agent reinforcement learning in Markov Decision Processes (MDPs). However, for multi-agent reinforcement learning in Markov games, the current best known sample complexity for model-based algorithms is rather suboptimal and compares unfavorably against recent model-free approaches. In this paper, we present a sharp analysis of model-based self-play algorithms for multi-agent Markov games. We design an algorithm \emph{Optimistic Nash Value Iteration} (Nash-VI) for two-player zero-sum Markov games that is able to output an $\epsilon$-approximate Nash policy in $\tilde{\mathcal{O}}(H^3SAB/\epsilon^2)$ episodes of game playing, where $S$ is the number of states, $A,B$ are the number of actions for the two players respectively, and $H$ is the horizon length. This significantly improves over the best known model-based guarantee of $\tilde{\mathcal{O}}(H^4S^2AB/\epsilon^2)$, and is the first that matches the information-theoretic lower bound $\Omega(H^3S(A+B)/\epsilon^2)$ except for a $\min\{A,B\}$ factor. In addition, our guarantee compares favorably against the best known model-free algorithm if $\min\{A,B\}=o(H^3)$, and outputs a single Markov policy while existing sample-efficient model-free algorithms output a nested mixture of Markov policies that is in general non-Markov and rather inconvenient to store and execute. We further adapt our analysis to designing a provably efficient task-agnostic algorithm for zero-sum Markov games, and designing the first line of provably sample-efficient algorithms for multi-player general-sum Markov games.
APA
Liu, Q., Yu, T., Bai, Y. & Jin, C.. (2021). A Sharp Analysis of Model-based Reinforcement Learning with Self-Play. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:7001-7010 Available from https://proceedings.mlr.press/v139/liu21z.html.

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