  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.
