Date of Original Version
Abstract or Table of Contents
Promising approaches to structured learning problems have recently been developed in the maximum margin framework. Unfortunately, algorithms that are computationally and memory eﬃcient enough to solve large scale problems have lagged behind. We propose using simple subgradient-based techniques for optimizing a regularized risk formulation of these problems in both online and batch settings, and analyze the theoretical convergence, generalization, and robustness properties of the resulting techniques. These algorithms are are simple, memory eﬃcient, fast to converge, and have small regret in the online setting. We also investigate a novel convex regression formulation of structured learning. Finally, we demonstrate the beneﬁts of the subgradient approach on three structured prediction problems.