The Interplay of Optimization and Machine Learning Research

The fields of machine learning and mathematical programming are increasingly intertwined. Optimization problems lie at the heart of most machine learning approaches. The Special Topic on Machine Learning and Large Scale Optimization examines this interplay. Machine learning researchers have embraced the advances in mathematical programming allowing new types of models to be pursued. The special topic includes models using quadratic, linear, second-order cone, semidefinite, and semi-infinite programs. We observe that the qualities of good optimization algorithms from the machine learning and optimization perspectives can be quite different. Mathematical programming puts a premium on accuracy, speed, and robustness. Since generalization is the bottom line in machine learning and training is normally done off-line, accuracy and small speed improvements are of little concern in machine learning. Machine learning prefers simpler algorithms that work in reasonable computational time for specific classes of problems. Reducing machine learning problems to well-explored mathematical programming classes with robust general purpose optimization codes allows machine learning researchers to rapidly develop new techniques. In turn, machine learning presents new challenges to mathematical programming. The special issue include papers from two primary themes: novel machine learning models and novel optimization approaches for existing models. Many papers blend both themes, making small changes in the underlying core mathematical program that enable the develop of effective new algorithms.