Smooth Boosting and Learning with Malicious Noise

Abstract

We describe a new boosting algorithm which generates only smooth distributions which do not assign too much weight to any single example. We show that this new boosting algorithm can be used to construct efficient PAC learning algorithms which tolerate relatively high rates of malicious noise. In particular, we use the new smooth boosting algorithm to construct malicious noise tolerant versions of the PACmodel p -norm linear threshold learning algorithms described in [ 23 ]. The bounds on sample complexity and malicious noise tolerance of these new PAC algorithms closely correspond to known bounds for the online pnorm algorithms of Grove, Littlestone and Schuurmans [ 14 ] and Gentile and Littlestone [ 13 ]. As special cases of our new algorithms we obtain linear threshold learning algorithms which match the sample complexity and malicious noise tolerance of the online Perceptron and Winnow algorithms. Our analysis reveals an interesting connection between boosting and noise tolerance in the PAC setting.