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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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.
The Arcade Learning Environment3 is available open source at https://github.com/mgbellemare/Arcade-Learning-Environment. The Go and chess environments are available open source in OpenSpiel52 at https://github.com/deepmind/open_spiel. The pseudocode for the MuZero algorithm can be found in the file pseudocode.py 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.
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.
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.
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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). https://doi.org/10.1038/s41586-020-03051-4