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Solving the Rubik’s cube with deep reinforcement learning and search


The Rubik’s cube is a prototypical combinatorial puzzle that has a large state space with a single goal state. The goal state is unlikely to be accessed using sequences of randomly generated moves, posing unique challenges for machine learning. We solve the Rubik’s cube with DeepCubeA, a deep reinforcement learning approach that learns how to solve increasingly difficult states in reverse from the goal state without any specific domain knowledge. DeepCubeA solves 100% of all test configurations, finding a shortest path to the goal state 60.3% of the time. DeepCubeA generalizes to other combinatorial puzzles and is able to solve the 15 puzzle, 24 puzzle, 35 puzzle, 48 puzzle, Lights Out and Sokoban, finding a shortest path in the majority of verifiable cases.

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Fig. 1: Visualization of scrambled states and goal states.
Fig. 2: The performance of DeepCubeA versus PDBs when solving the Rubik’s cube with BWAS.
Fig. 3: The performance of DeepCubeA.
Fig. 4: An example of symmetric solutions that DeepCubeA finds to symmetric states.

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Data availability

The environments for all puzzles presented in this paper, code to generate labelled training data and initial states used to test DeepCubeA are available through a Code Ocean compute capsule (


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The authors thank D.L. Flores for useful suggestions regarding the DeepCubeA server and T. Rokicki for useful suggestions and help with the optimal Rubik’s cube solver.

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P.B. designed and directed the project. F.A., S.M. and A.S. contributed equally to the development and testing of DeepCubeA. All authors contributed to writing and editing the paper.

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Correspondence to Pierre Baldi.

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The authors declare no competing interests.

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Agostinelli, F., McAleer, S., Shmakov, A. et al. Solving the Rubik’s cube with deep reinforcement learning and search. Nat Mach Intell 1, 356–363 (2019).

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