Optimal Convergence Rate in Feed Forward Neural Networks using HJB Equation

TL;DR

This paper introduces a control theoretic method using the Hamilton-Jacobi-Bellman equation to derive optimal weight updates in feed-forward neural networks, achieving faster convergence and potential for global optimization.

Contribution

It provides closed-form solutions for optimal weight updates in feed-forward neural networks using HJB, enhancing convergence speed and global optimization potential.

Findings

Faster convergence compared to existing algorithms

Validated on benchmark datasets like parity, breast cancer, and credit approval

Discusses global optimization capabilities of HJB-based updates

Abstract

A control theoretic approach is presented in this paper for both batch and instantaneous updates of weights in feed-forward neural networks. The popular Hamilton-Jacobi-Bellman (HJB) equation has been used to generate an optimal weight update law. The remarkable contribution in this paper is that closed form solutions for both optimal cost and weight update can be achieved for any feed-forward network using HJB equation in a simple yet elegant manner. The proposed approach has been compared with some of the existing best performing learning algorithms. It is found as expected that the proposed approach is faster in convergence in terms of computational time. Some of the benchmark test data such as 8-bit parity, breast cancer and credit approval, as well as 2D Gabor function have been used to validate our claims. The paper also discusses issues related to global optimization. The limitations of popular deterministic weight update laws are critiqued and the possibility of global optimization using HJB formulation is discussed. It is hoped that the proposed algorithm will bring in a lot of interest in researchers working in developing fast learning algorithms and global optimization.