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arXiv 2002.03555cs.LGstat.ML
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监督学习:不输不哭

Supervised Learning: No Loss No Cry

Google Research(谷歌研究院)

Richard Nock, Aditya Krishna Menon

摘要:

监督学习需要指定一个损失函数来最小化。虽然从计算和统计的角度来看,可容许损失的理论已经发展得很好,但这些理论提供了一整套不同的选择。在实践中,该选择通常以\emph{ad hoc}方式进行。为了使该过程更有原则,针对下游任务的\emph{learning the loss function}问题(例如,分类)最近引起了人们的兴趣。然而,这方面的工作一般都是经验性的。在本文中,我们通过一个新的镜头重新审视了Kakade等人(2011)的{ \sc SLISotron}算法,推导出基于Bregman分歧的推广,并展示了它如何提供学习损失的原则性程序。详细地说,我们将{ \sc SLISotron}转换为从复合平方损失族中学习损失。通过解释这一点,通过镜头的\emph{proper losses},我们得到了推广的{ \sc SLISotron}的基础上Bregman分歧。所得到的{ \sc BregmanTron}算法与分类器一起共同学习损失。它配备了一个简单的收敛保证,它学习的损失,它的一组可能的输出带有贝叶斯规则的不可知近似性的保证。实验表明,{ \sc BregmanTron}大大优于{ \sc SLISotron},它学习的损失可以通过其他算法最小化不同的任务,从而打开域之间的有趣的问题\textit{loss transfer}。

英文摘要:

Supervised learning requires the specification of a loss function to minimise. While the theory of admissible losses from both a computational and statistical perspective is well-developed, these offer a panoply of different choices. In practice, this choice is typically made in an \emph{ad hoc} manner. In hopes of making this procedure more principled, the problem of \emph{learning the loss function} for a downstream task (e.g., classification) has garnered recent interest. However, works in this area have been generally empirical in nature. In this paper, we revisit the {\sc SLIsotron} algorithm of Kakade et al. (2011) through a novel lens, derive a generalisation based on Bregman divergences, and show how it provides a principled procedure for learning the loss. In detail, we cast {\sc SLIsotron} as learning a loss from a family of composite square losses. By interpreting this through the lens of \emph{proper losses}, we derive a generalisation of {\sc SLIsotron} based on Bregman divergences. The resulting {\sc BregmanTron} algorithm jointly learns the loss along with the classifier. It comes equipped with a simple guarantee of convergence for the loss it learns, and its set of possible outputs comes with a guarantee of agnostic approximability of Bayes rule. Experiments indicate that the {\sc BregmanTron} substantially outperforms the {\sc SLIsotron}, and that the loss it learns can be minimized by other algorithms for different tasks, thereby opening the interesting problem of \textit{loss transfer} between domains.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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