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 a broad subset of algorithms in this class, including both Perceptron and Winnow, but also many new algorithms. Our proof hinges on analyzing a generic measure of progress construction that gives insight as to when and how such algorithms converge.