Gradient Descent Algorithm Optimization and its Application in Linear Regression Model

This paper systematically analyzes the application of gradient descent algorithm in linear regression model and proposes a variety of optimization methods. The basic concepts and mathematical expressions of linear regression model are introduced, and the basic principles and mathematical derivation of gradient descent algorithm are explained. The specific application of gradient descent algorithm in parameter estimation and model optimization is discussed, especially in big data environment. Several optimization methods of gradient descent algorithm are proposed, including learning rate adjustment, momentum method, RMSProp and Adam optimization algorithm. This paper discusses the advantages and disadvantages of gradient descent algorithm and its challenges in practical application, and proposes future research directions. The research results show that the improved gradient descent algorithm has higher computational efficiency and better convergence when processing large-scale data and complex models.