This work applies reinforcement learning (RL) from the AI machine learning field to derive an optimal Bitcoin-like blockchain mining strategy without knowing the details of the blockchain network model. Previously, the most profitable mining strategy was believed to be honest mining encoded in the default blockchain protocol. It was shown later that it is possible to gain more mining rewards by deviating from honest mining. In particular, the mining problem can be formulated as a Markov Decision Process (MDP) which can be solved to give the optimal mining strategy. However, solving the mining MDP requires knowing the values of various parameters that characterize the blockchain network model. In real blockchain networks, these parameter values are not easy to obtain and may change over time. This hinders the use of the MDP model-based solution. In this work, we employ RL to dynamically learn a mining strategy with performance approaching that of the optimal mining strategy by observing and interacting with the network. Since the mining MDP problem has a non-linear objective function (rather than linear functions of standard MDP problems), we design a new multi-dimensional RL algorithm to solve the problem. Experimental results indicate that, without knowing the parameter values of the mining MDP model, our multi-dimensional RL mining algorithm can still achieve the optimal performance over time-varying blockchain networks.