Hedging Structured Concepts

We develop an online algorithm called Component Hedge for learning structured concept classes when the loss of a structured concept sums over its components. Example classes include paths through a graph (composed of edges) and partial permutations (composed of assignments). The algorithm maintains a parameter vector with one non-negative weight per component, which always lies in the convex hull of the structured concept class. The algorithm predicts by decomposing the current parameter vector into a convex combination of concepts and choosing one of those concepts at random. The parameters are updated by first performing a multiplicative update and then projecting back into the convex hull. We show that Component Hedge has optimal regret bounds for a large variety of structured concept classes.

• Type: Journal
• Year: 2010
• Where: COLT
• Authors: Wouter M. Koolen, Manfred K. Warmuth, Jyrki Kivinen
• Keywords: COLT 2010, Convex Hull, Machine Learning, Parameter Vector, Structured Concept