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Mastering Atari, Go, chess and shogi by planning with a learned model


Constructing agents with planning capabilities has long been one of the main challenges in the pursuit of artificial intelligence. Tree-based planning methods have enjoyed huge success in challenging domains, such as chess1 and Go2, where a perfect simulator is available. However, in real-world problems, the dynamics governing the environment are often complex and unknown. Here we present the MuZero algorithm, which, by combining a tree-based search with a learned model, achieves superhuman performance in a range of challenging and visually complex domains, without any knowledge of their underlying dynamics. The MuZero algorithm learns an iterable model that produces predictions relevant to planning: the action-selection policy, the value function and the reward. When evaluated on 57 different Atari games3—the canonical video game environment for testing artificial intelligence techniques, in which model-based planning approaches have historically struggled4—the MuZero algorithm achieved state-of-the-art performance. When evaluated on Go, chess and shogi—canonical environments for high-performance planning—the MuZero algorithm matched, without any knowledge of the game dynamics, the superhuman performance of the AlphaZero algorithm5 that was supplied with the rules of the game.

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Fig. 1: Planning, acting and training with a learned model.
Fig. 2: Evaluation of MuZero throughout training in chess, shogi, Go and Atari.
Fig. 3: Evaluations of MuZero on Go, all 57 Atari games and Ms. Pac-Man.

Data availability

MuZero is trained only on data generated by MuZero itself; no external data were used to produce the results presented in the article. Data for all figures and tables presented are available in JSON format in the Supplementary Information.

Code availability

The Arcade Learning Environment3 is available open source at The Go and chess environments are available open source in OpenSpiel52 at The pseudocode for the MuZero algorithm can be found in the file in the Supplementary Information. All the neural architecture details and hyperparameters are described in Methods.


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We thank L. Bennett, O. Smith and C. Apps for organizational assistance; K. Kavukcuoglu for reviewing the paper; T. Anthony, M. Lai, N. Tomasev, U. Paquet, S. Ghaisas for many discussions; and the rest of the DeepMind team for their support.

Author information




J.S., I.A., T.H. and D.S. designed the MuZero algorithm with advice from A.G., K.S., L.S., E.L., T.L. and T.G.; J.S., I.A., T.H. and S.S. implemented the MuZero program, ran experiments and analysed data. D.S., J.S., I.A. and T.H. wrote the paper with contributions from A.G., K.S., L.S., E.L., T.L., T.G. and D.H.

Corresponding author

Correspondence to David Silver.

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Competing interests

DeepMind filed Greek patent GR20200100037 on 28 January 2020, covering the MuZero algorithm described in this paper, listing the authors J.S., I.A. and T.H. as inventors. The other authors declare no competing interests.

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Peer review information Nature thanks Jaap van den Herik and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

This file contains Supplementary Figures S1-S5 and Supplementary Tables S1-S2.

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Schrittwieser, J., Antonoglou, I., Hubert, T. et al. Mastering Atari, Go, chess and shogi by planning with a learned model. Nature 588, 604–609 (2020).

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