Machine learning problems from optimization perspective

Both optimization and learning play important roles in a system for intelligent tasks. On one hand, we introduce three types of optimization tasks studied in the machine learning literature, corresponding to the three levels of inverse problems in an intelligent system. Also, we discuss three major roles of convexity in machine learning, either directly towards a convex programming or approximately transferring a difficult problem into a tractable one in help of local convexity and convex duality. No doubly, a good optimization algorithm takes an essential role in a learning process and new developments in the literature of optimization may thrust the advances of machine learning. On the other hand, we also interpret that the key task of learning is not simply optimization, as sometimes misunderstood in the optimization literature. We introduce the key challenges of learning and the current status of efforts towards the challenges. Furthermore, learning versus optimization has also been examined from a unified perspective under the name of Bayesian Ying-Yang learning, with combinatorial optimization made more effectively in help of learning.