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This paper presents a coarse coding technique and an action selection scheme for reinforcement learning (RL) in multi-dimensional and continuous state-action spaces following conventional and sound RL manners. RL in high- dimensional continuous domains includes two issues: one is a generalization problem for value-function approximation, and the other is a sampling problem for action selection over multi-dimensional continuous action spaces. The proposed method combines random rectangular coarse coding with an action selection scheme using Gibbs-sampling. The random rectangular coarse coding is very simple and quite suited both to approximate Q-functions in high-dimensional spaces and to execute Gibbs sampling. Gibbs sampling enables us to execute action selection following Boltsmann distribution over high-dimensional action space.