Faster Rates for training Max-Margin Markov Networks

TL;DR

This paper introduces a new optimization technique for max-margin Markov networks that achieves faster convergence rates by leveraging Bregman projections, improving efficiency in structured output prediction tasks.

Contribution

The paper proposes a novel excessive gap reduction method based on Bregman projections that converges faster and maintains graphical model factorization, unlike previous approaches.

Findings

Converges in O(1/√ε) iterations, faster than previous methods.

Preserves graphical model factorization for tractable computation.

Easily kernelized for enhanced flexibility.

Abstract

Structured output prediction is an important machine learning problem both in theory and practice, and the max-margin Markov network (\mcn) is an effective approach. All state-of-the-art algorithms for optimizing \mcn\ objectives take at least $O(1/\epsilon)$ number of iterations to find an $\epsilon$ accurate solution. Recent results in structured optimization suggest that faster rates are possible by exploiting the structure of the objective function. Towards this end \citet{Nesterov05} proposed an excessive gap reduction technique based on Euclidean projections which converges in $O(1/\sqrt{\epsilon})$ iterations on strongly convex functions. Unfortunately when applied to \mcn s, this approach does not admit graphical model factorization which, as in many existing algorithms, is crucial for keeping the cost per iteration tractable. In this paper, we present a new excessive gap reduction technique based on Bregman projections which admits graphical model factorization naturally, and converges in $O(1/\sqrt{\epsilon})$ iterations. Compared with existing algorithms, the convergence rate of our method has better dependence on $\epsilon$ and other parameters of the problem, and can be easily kernelized.