Comparison of the efficiency of zero and first order minimization methods in neural networks

Abstract

To minimize the objective function in neural networks, first-order methods are usually used, which involve the repeated calculation of the gradient. The number of variables in modern neural networks can be many thousands and even millions. Numerous experiments show that the analytical calculation time of an N variable function’s gradient is approximately N/5 times longer than the calculation time of the function itself. The article considers the possibility of using zero-order methods to minimize the function. In particular, a new zero-order method for function minimization, descent over two-dimensional spaces, is proposed. The convergence rates of three different methods are compared: standard gradient descent with automatic step selection, coordinate descent with step selection for each coordinate, and descent over two-dimensional subspaces. It has been shown that the efficiency of properly organized zero-order methods in the considered problems of training neural networks is not lower than the gradient ones.

Keywords

• neural networks
• objective function
• minimization
• gradient
• gradient descent
• coordinate descent
• convergence rate