Machine Learning under a Modern Optimization Lens
Dimitris Bertsimas, (MIT)
We use modern optimization methods to address a variety of ML problems:
1) We transform sparse regression problems to convex mixed-integer optimization problems, which we solve via cutting planes efficiently for a number of points and factors in the 100,000s.
2) We show how these ideas extend to the matrix and tensor completion.
3) We propose a robust optimization framework for optimally selecting the training and validation sets for regression problems and show that it leads to lower prediction error and lower standard deviation for both the prediction and the coefficients compared to the usual randomization approach.
Dimitris Bertsimas is currently the Boeing Professor of Operations Research, the Associate Dean of Business Analytics at the Sloan School of Management, MIT. He received his SM and PhD in Applied Mathematics and Operations Research from MIT in 1987 and 1988 respectively. He has been with the MIT faculty since 1988. His research interests include optimization, machine learning and applied probability and their applications in health care, finance, operations management and transportation. He has co-authored more than 200 scientific papers and five graduate-level textbooks. He is the editor in Chief of INFORMS Journal of Optimization and former department editor in Optimization for Management Science and in Financial Engineering in Operations Research. He has supervised 76 doctoral students and he is currently supervising 25 others. He is a member of the National Academy of Engineering since 2005, an INFORMS fellow, and he has received numerous research and teaching awards including the John von Neumann theory prize for fundamental, sustained contributions to the theory of operations research and the management sciences and the president's award of INFORMS recognizing important contributions to the welfare of society, both in 2019.