Solutions to Selected Problems In : Reinforcement Learning : An Introduction by

We could improve our reinforcement learning algorithm by taking advantage of symmetry by simplifying the definition of the “state” and “action” upon which the algorithm would works. By simplifying the state in such a way that the dimension decreases we can be more confident that our learned results will be statistically significant since the state space we operate in is reduced. If our opponent was taking advantage of symmetries in the game tic-tac-toe our algorithm should also since this fact, would enable us to be a better game player against this type of player. If our player does not use symmetries then our algorithm should not either (except to reduce the state space as discussed above) since enforcing a symmetry on our opponent (that is not in fact there) should decrease our performance when playing against this type of opponent.