This paper introduces algorithms for learning how to trade using insider (superior) information in Kyle's model of financial markets. Prior results in finance theory relied on the insider having perfect knowledge of the structure and parameters of the market. I show here that it is possible to learn the equilibrium trading strategy when its form is known even without knowledge of the parameters governing trading in the model. However, the rate of convergence to equilibrium is slow, and an approximate algorithm that does not converge to the equilibrium strategy achieves better utility when the horizon is limited. I analyze this approximate algorithm from the perspective of reinforcement learning and discuss the importance of domain knowledge in designing a successful learning algorithm. Categories and Subject Descriptors J.4 [Social and Behavioral Sciences]: Economics General Terms Economics Keywords Computational Finance, Market Microstructure