论文标题
通过乘数的交替方向方法优化多任务学习的评估指标
Optimizing Evaluation Metrics for Multi-Task Learning via the Alternating Direction Method of Multipliers
论文作者
论文摘要
多任务学习(MTL)旨在通过利用共享因素来提高多个任务的概括性能。使用各种指标(例如,F-Score,ROC曲线下的面积)来评估MTL方法的性能。大多数现有的MTL方法试图最大程度地减少分类错误的错误分类错误或回归的均方向错误。在本文中,我们提出了一种直接优化大型MTL问题的评估指标的方法。直接优化评估指标的MTL的公式是两个部分的组合:(1)在所有任务上定义的正规器,以捕获这些任务的相关性; (2)多个结构化铰链损耗的总和,每个损耗对应于一个任务上的某些评估度量的替代品。这种表述在优化方面具有挑战性,因为它的两个部分都是非平滑的。为了解决这个问题,我们提出了一个基于乘数的交替方向方案的新型优化程序,在该过程中,我们将整个优化问题分解为对应于正规机的子问题,以及与结构化铰链损耗相对应的另一个子问题。对于大型MTL问题,第一个子问题具有封闭形式的解决方案。为了解决第二个子问题,我们通过坐标提出了有效的原始二偶有算法。广泛的评估结果表明,在大量的MTL问题中,提出的直接优化评估指标的MTL方法具有针对相应基线方法的较高性能提高。
Multi-task learning (MTL) aims to improve the generalization performance of multiple tasks by exploiting the shared factors among them. Various metrics (e.g., F-score, Area Under the ROC Curve) are used to evaluate the performances of MTL methods. Most existing MTL methods try to minimize either the misclassified errors for classification or the mean squared errors for regression. In this paper, we propose a method to directly optimize the evaluation metrics for a large family of MTL problems. The formulation of MTL that directly optimizes evaluation metrics is the combination of two parts: (1) a regularizer defined on the weight matrix over all tasks, in order to capture the relatedness of these tasks; (2) a sum of multiple structured hinge losses, each corresponding to a surrogate of some evaluation metric on one task. This formulation is challenging in optimization because both of its parts are non-smooth. To tackle this issue, we propose a novel optimization procedure based on the alternating direction scheme of multipliers, where we decompose the whole optimization problem into a sub-problem corresponding to the regularizer and another sub-problem corresponding to the structured hinge losses. For a large family of MTL problems, the first sub-problem has closed-form solutions. To solve the second sub-problem, we propose an efficient primal-dual algorithm via coordinate ascent. Extensive evaluation results demonstrate that, in a large family of MTL problems, the proposed MTL method of directly optimization evaluation metrics has superior performance gains against the corresponding baseline methods.