Hoo Optimality Criteria for LMS and Backpropagation

Part of Advances in Neural Information Processing Systems 6 (NIPS 1993)

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Authors

Babak Hassibi, Ali H. Sayed, Thomas Kailath

Abstract

We have recently shown that the widely known LMS algorithm is an H OO optimal estimator. The H OO criterion has been introduced, initially in the control theory literature, as a means to ensure ro(cid:173) bust performance in the face of model uncertainties and lack of statistical information on the exogenous signals. We extend here our analysis to the nonlinear setting often encountered in neural networks, and show that the backpropagation algorithm is locally H OO optimal. This fact provides a theoretical justification of the widely observed excellent robustness properties of the LMS and backpropagation algorithms. We further discuss some implications of these results.