Tracking capabilities of single-layer threshold networks when confronted with drift and random noise

This paper analyzes the tracking performance for single layer threshold neural networks when the weights of a target network change slowly with time. Two different adversaries that control target network changes are considered: a random unbiased adversary, and a worst case adversary. Four different tracking algorithms are considered and are divided into two classes: conservative (including the optimal conservative algorithm and the Perceptron algorithm) and nonconservative (including the optimal nonconservative algorithm and the LMS algorithm). The steady-state generalization error is used to evaluate the performance of tracking algorithms. Upper bounds on the generalization error are derived for the four tracking algorithms when confronted with each adversary. The LMS algorithm is also studied when confronted with random drift and additive noise. Analytical results are verified through computer simulations