General convergence results for linear discriminant updates

The problem of learning linear discriminant concepts can be solved by various mistake-driven update procedures, including the Winnow family of algorithms and the well-known Perceptron algorithm. In this paper we define the general class of quasi-additive algorithms, which includes Perceptron and Winnow as special cases. We give a single proof of convergence that covers much of this class, including both Perceptron and Winnow but also many novel algorithms. Our proof introduces a generic measure of progress that seems to capture much of when and how these algorithms converge. Using this measure, we develop a simple general technique for proving mistake bounds, which we apply to the new algorithms as well as existing algorithms.