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Rubik's Cube Environment#

We provide here a Jax JIT-able implementation of the Rubik's cube. The environment contains an implementation of the classic 3x3x3 cube by default, and configurably other sizes. The goal of the agent is to match all stickers on each face to a single colour. On resetting the environment the cube will be randomly scrambled with a configurable number of turns (by default 100).

Observation#

The observation given to the agent gives a view of the current state of the cube,

  • cube: jax array (int8) of shape (6, cube_size, cube_size) whose values are in [0, 1, 2, 3, 4, 5] (corresponding to the different sticker colors). The indices of the array specify the sticker position - first the face (in the order up, front, right, back, left, down) and then the row and column. Note that the orientation of each face is as follows:

    • UP: LEFT face on the left and BACK face pointing up

    • FRONT: LEFT face on the left and UP face pointing up

    • RIGHT: FRONT face on the left and UP face pointing up

    • BACK: RIGHT face on the left and UP face pointing up

    • LEFT: BACK face on the left and UP face pointing up

    • DOWN: LEFT face on the left and FRONT face pointing up

  • step_count: jax array (int32) of shape (), representing the number of steps in the episode thus far.

Action#

The action space is a MultiDiscreteArray, specifically a tuple of an index between 0 and 5 (since there are 6 faces), an index between 0 and cube_size//2 (the number of possible depths), and an index between 0 and 2 (3 possible directions). An action thus consists of three pieces of information:

  • Face to turn,

  • Depth of the turn (possible depths are between 0 representing the outer layer and cube_size//2 representing the layer closest to the middle),

  • Direction of turn (possible directions are clockwise, anti-clockwise, or a half turn).

Reward#

The reward function is configurable, but by default is the fully sparse reward giving +1 for solving the cube and otherwise 0. The episode terminates if either the cube is solved or a configurable horizon (by default 200) is reached.

Registered Versions 📖#

  • RubiksCube-v0, the standard Rubik's Cube puzzle with faces of size 3x3.

  • RubiksCube-partly-scrambled-v0, an easier version of the standard Rubik's Cube puzzle with faces of size 3x3 yet only 7 scrambles at reset time, making it technically maximum 7 actions away from the solution.

Last update: 2024-03-29
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