Abstract: We present a machine learning approach to predict the strategy behind the optimal solution of continuous and mixed-integer convex optimization problems. Using interpretable algorithms such as optimal classification trees we gain insights on the relationship between the problem data and the optimal solution. In this way, optimization is no longer a black-box and practitioners can understand it. Moreover, our method is able to compute the optimal solutions at very high speed. This applies also to non-interpretable machine learning techniques such as neural networks since they can be evaluated very efficiently. We benchmark our approach on several examples obtaining accuracy above 90% and computation times multiple orders of magnitude faster than state-of-the-art solvers. Therefore, our method provides on the one hand a novel insightful understanding of the optimal strategies to solve a broad class of continuous and mixed-integer optimization problems and on the other hand a powerful computational tool to solve online optimization at very high speed.

Bio: Bartolomeo Stellato is a Postdoctoral Associate at the MIT Sloan School of Management in the Operations Research Center under the supervision of Prof. Dimitris Bertsimas. His research focuses on the interplay between machine learning and optimization. He is also interested in fast numerical methods for online optimization. He obtained his D.Phil. (Ph.D.) in Engineering Science (2017) from the University of Oxford under the supervision of Prof. Paul Goulart as part of the Marie Curie EU project TEMPO. He received a B.Sc. degree in Automation Engineering (2012) from Politecnico di Milano and a M.Sc. in Robotics, Systems and Control (2014) from ETH Zürich. In 2016, he visited Prof. Stephen Boyd’s group at Stanford University where he developed the OSQP solver which is now widely used in academia and industry with more than one million downloads. He is the recipient of the 2017 IEEE Transaction on Power Electronics 1st Prize Paper Award.