Efficacy of Regularized Multitask Learning Based on SVM Models

This article investigates the efficacy of a regularized multitask learning (MTL) framework based on SVM (M-SVM) to answer whether MTL always provides reliable results and how MTL outperforms independent learning. We first find that the M-SVM is Bayes risk consistent in the limit of a large sample size. This implies that despite the task dissimilarities, the M-SVM always produces a reliable decision rule for each task in terms of the misclassification error when the data size is large enough. Furthermore, we find that the task-interaction vanishes as the data size goes to infinity, and the convergence rates of the M-SVM and its single-task counterpart have the same upper bound. The former suggests that the M-SVM cannot improve the limit classifier's performance; based on the latter, we conjecture that the optimal convergence rate is not improved when the task number is fixed. As a novel insight into MTL, our theoretical and experimental results achieved an excellent agreement that the benefit of the MTL methods lies in the improvement of the preconvergence-rate (PCR) factor (to be denoted in Section III) rather than the convergence rate. Moreover, this improvement of PCR factors is more significant when the data size is small. In addition, our experimental results of five other MTL methods demonstrate the generality of this new insight.