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Many reinforcement learning methods are based on a function Q (s ,a ) whose value is the discounted total reward expected after performing the action a in the state s . This paper explores the implications of representing the Q function as Q (s ,a )=s T Wa , where W is a matrix that is learned. In this representation, both s and a are real-valued vectors that may have high dimension. We show that action selection can be done using standard linear programming, and that W can be learned using standard linear regression in the algorithm known as fitted Q iteration. Experimentally, the resulting method learns to solve the mountain car task in a sample-efficient way. The same method is also applicable to an inventory management task where the state space and the action space are continuous and high-dimensional.