Performance Bounds for Single Layer Threshold Networks when Tracking a Drifting Adversary

Abstract

This paper finds upper bounds for the generalization error of three tracking algorithms when confronted with a worst case adversary. A system identification model is used where both the target and tracking network are single layer threshold networks, with the target weights changing slowly (the drift problem). Previous work considered random unbiased drifting adversaries. This paper focuses on the analysis of a worst case drifting adversary. For a small drift rate of γ, we find that upper bounds for the optimal conservative tracker, the perceptron tracker, and the least mean square (LMS) tracker are respectively 2γ/cos(γπ),2γn/πcos(γπ), and γ(2n + 2.5) where n is the number of inputs. Simulation results validate the analysis and also show that the bounds are tight when γ is small for the perceptron and LMS tracker. The effects of additive noise, correlated inputs and non-Gaussian inputs are also discussed. © 1997 Elsevier Science Ltd.