The Solution of Semi-Infinite Linear Programs Using Boosting-Like Methods

Gunnar Rätsch

Abstract: We consider methods for the solution of large linear optimization problems, in particular so-called Semi-Infinite Linear Programs (SILPs) that have a finite number of variables but infinitely many linear constraints. We illustrate that such optimization problems frequently appear in machine learning and discuss several examples including maximum margin boosting, multiple kernel learning and structure learning. In the second part we review methods for solving SILPs. Here, we are particularly interested in methods related to boosting. We review recent theoretical results concerning the convergence of these algorithms and conclude this work with a discussion of empirical results comparing these algorithms.