As an alternative to rational expectations, adaptive learning was widely used to build macroeconomic models. Adaptive learning could be assumed that economic agents like econometricians could use statistical or econometric models to form their own expectations. However, the accuracy of expectation was closely related to the adaptive learning algorithm. The adaptive learning literature was referred and disentangled, and based on least squares algorithm of a derived variable forgetting factor, the theoretical derivation of two common adaptive learning algorithms was proposed, in order to provide some reference for the future research.