## On Online Learning of Decision Lists

** Ziv Nevo, Ran El-Yaniv**;
3(Oct):271-301, 2002.

### Abstract

A fundamental open problem in computational learning theory is whether there is an attribute efficient learning algorithm for the concept class of decision lists (Rivest, 1987; Blum, 1996). We consider a weaker problem, where the concept class is restricted to decision lists with*D*alternations. For this class, we present a novel online algorithm that achieves a mistake bound of

*O*(

*r*

^{D}/log

*n*), where

*r*is the number of relevant variables, and

*n*is the total number of variables. The algorithm can be viewed as a strict generalization of the famous Winnow algorithm by Littlestone (1988), and improves the

*O*(

*r*^(2

*D*)/log

*n*) mistake bound of Balanced Winnow. Our bound is stronger than a similar PAC-learning result of Dhagat and Hellerstein (1994). A combination of our algorithm with the algorithm suggested by Rivest (1987) might achieve even better bounds.