Optimal Transport and Minimax Optimization
We first consider a motivational perspective on the mathematical foundations of learning and decision making, spanning a broad spectrum from various fields of mathematics through various applications of learning and decision making. Within this context, we then focus on some recent advances in optimal transport, probability, minimax optimization and computational methods that support the mathematical foundations of learning. This includes a brief overview of minimax formulations and theoretical results for a couple of motivating problems related to statistical convergence and transfer learning. We next consider distributionally robust optimization formulations and solutions of motivating problems related to model generalization and input model uncertainty, together with associated theoretical results and efficient algorithms that balance fundamental tradeoffs between computation and stochastic error. Empirical results further demonstrate and quantify the significant benefits of our solution approaches over previous related work in learning model generalization and nonconvex portfolio choice modeling under cumulative prospect theory.
Mark S. Squillante is a Distinguished Research Staff Member and the Manager of Foundations of Probability, Dynamics, and Control within the Mathematical Sciences of IBM Research at the Thomas J. Watson Research Center. He has been an adjunct faculty member in the School of Operations Research and Information Engineering at Cornell Tech and the School of Engineering and Applied Science at Columbia University. His research interests broadly concern mathematical foundations of the analysis, modeling and optimization of the design and control of complex systems under uncertainty, and their broad applications. Mark is an elected Fellow of INFORMS, ACM, IEEE and AAIA, and recipient of the (Biennial) Best Publication in Applied Probability Award (INFORMS Applied Probability Society), the Daniel H. Wagner Prize (INFORMS), 9 best paper awards, 27 major IBM technical awards, and 40 IBM invention awards. He currently serves as Editor-in-Chief of Stochastic Models, as Chair of IFIP Working Group 7.3, on the INFORMS Subdivisions Council, and on the Board of Directors of the American Automatic Control Council. He received a Ph.D. degree from the University of Washington.