This paper surveys the machine learning literature and presents machine learning as optimization models. Such models can benefit from the advancement of numerical optimization techniques which have already played a distinctive role in several machine learning settings. Particularly, mathematical optimization models are presented for commonly used machine learning approaches for regression, classification, clustering, and deep neural networks as well new emerging applications in machine teaching and empirical model learning. The strengths and the shortcomings of these models are discussed and potential research directions are highlighted.

翻译：本文对机器学习文献进行了调查,并将机器学习作为优化模型提出来,这些模型可受益于数字优化技术的进步,这些技术在一些机器学习环境中已经发挥了独特的作用,特别是,提出了数学优化模型,用于常用的机器学习方法,用于回归、分类、集群和深层神经网络,以及在机器教学和实证模型学习方面新出现的应用,讨论了这些模型的长处和缺点,并强调了潜在的研究方向。