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Solving Rubik's cube can be thought of as a Planning problem which has :

  • a state space $S$
  • a set $G \subseteq S$ of goal states (in this case singleton)
  • actions $A(s) \subseteq A$ applicable in each states in $S$
  • action costs $c(a, s)>0$ (optional)
  • discount factor $\gamma$ (optional)

On the other hand a MDP has an extra point:

  • transition probabilities $P_a(s'|s)$ for $s\in S$ and $a\in A(s)$

So can solution to Rubik's cube be seen from the point of view of Markov Decision Process ? What are the practical problems where principles of solving Rubik's cube can be applied ?

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  • $\begingroup$ This question is a bit vague and broad. Could you better explain what you are looking for? Maybe provide some context? $\endgroup$ – A.P. Jun 10 '15 at 21:43
  • $\begingroup$ Let me know if any other clarification is needed $\endgroup$ – aroyc Jun 11 '15 at 17:02
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Yes, you could perfectly model that as a MDP. Keep in mind to specify a positive reward for all terminal/goal states.

However, I would say it will not be the most effective approach. If you are planning to use reinforcement learning, I see a few problems / disadvantages. Typically you use random exploration, but here it will not help much and a planning algorithm with a good heuristic would perform much better. Another issue is the amount of possible starting points that you will need to consider if you want to obtain a good generic policy.

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