Smoothing Multivariate Performance Measures

TL;DR

This paper introduces a smoothing strategy combined with Nesterov's accelerated gradient to optimize multivariate performance measures more efficiently, achieving faster convergence without losing accuracy.

Contribution

The paper presents a novel smoothing approach for multivariate performance scores that, when combined with accelerated gradient methods, improves convergence speed over existing cutting plane algorithms.

Findings

Faster convergence to an eta accurate solution compared to SVM-Perf and BMRM.

Maintains similar per-iteration computational cost as existing methods.

Empirical results show significant speedup without sacrificing generalization.

Abstract

A Support Vector Method for multivariate performance measures was recently introduced by Joachims (2005). The underlying optimization problem is currently solved using cutting plane methods such as SVM-Perf and BMRM. One can show that these algorithms converge to an eta accurate solution in O(1/Lambda*e) iterations, where lambda is the trade-off parameter between the regularizer and the loss function. We present a smoothing strategy for multivariate performance scores, in particular precision/recall break-even point and ROCArea. When combined with Nesterov's accelerated gradient algorithm our smoothing strategy yields an optimization algorithm which converges to an eta accurate solution in O(min{1/e,1/sqrt(lambda*e)}) iterations. Furthermore, the cost per iteration of our scheme is the same as that of SVM-Perf and BMRM. Empirical evaluation on a number of publicly available datasets shows that our method converges significantly faster than cutting plane methods without sacrificing generalization ability.