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A control theoretic approach is presented in this paper for both batch andinstantaneous updates of weights in feed-forward neural networks. The popularHamilton-Jacobi-Bellman (HJB) equation has been used to generate an optimalweight update law. The remarkable contribution in this paper is that closedform solutions for both optimal cost and weight update can be achieved for anyfeed-forward network using HJB equation in a simple yet elegant manner. Theproposed approach has been compared with some of the existing best performinglearning algorithms. It is found as expected that the proposed approach isfaster in convergence in terms of computational time. Some of the benchmarktest data such as 8-bit parity, breast cancer and credit approval, as well as2D Gabor function have been used to validate our claims. The paper alsodiscusses issues related to global optimization. The limitations of populardeterministic weight update laws are critiqued and the possibility of globaloptimization using HJB formulation is discussed. It is hoped that the proposedalgorithm will bring in a lot of interest in researchers working in developingfast learning algorithms and global optimization.

Optimal Convergence Rate in Feed Forward Neural Networks using HJB Equation