Bundle Methods for Machine Learning

Alexander J. Smola, S. V. N. Vishwanathan, Quoc V. Le

Abstract: We present a globally convergent method for regularized risk minimization problems. Our method applies to Support Vector estimation, regression, Gaussian Processes, and any other regularized risk minimization setting which leads to a convex optimization problem. SVMPerf can be shown to be a special case of our approach. In addition to the unified framework we present tight convergence bounds, which show that our algorithm converges in O(1/∊) steps to ∊ precision for general convex problems and in O(log(1/∊)) steps for continuously differentiable problems. We demonstrate in experiments the performance of our approach.