Theoretical Analysis of Learning Speed in Gradient Descent Algorithm Replacing Derivative with Constant

In on-line gradient descent learning, the local property of the derivative term of the output function can slowly converge. Improving the derivative term, such as by using the natural gradient, has been proposed for speeding up the convergence. Beside this sophisticated method, we propose an algorithm that replaces the derivative term with a constant and show that this greatly increases convergence speed when the learning step size is less than 2.7, which is near the optimal learning step size. The proposed algorithm is inspired by linear perceptron learning and can avoid locality of the derivative term. We derived the closed deterministic differential equations by using a statistical mechanics method and show the validity of theoretical results by comparing them with computer simulation solutions. In real problems, the optimum learning step size is not given in advance. Therefore, the learning step size must be small. The proposed method is useful in this case.