The overarching theme of my talk will be the study of different optimization problems and applications. I will first present how the theory of distributionally robust optimization provides a new perspective for understanding the regularization term in the estimation of precision matrices with the graphical lasso. This will motivate an alternative to cross-validation for the selection of the regularization parameter. Then, I will present an algorithm for the distributed computation of a Wasserstein barycenter – a principled way of “summarizing” a group of probability measures by solving an optimization problem in the Wasserstein space. Finally, if time allows, I will show the use of contraction theory – a strong stability tool used in control theory – to characterize the performance of the popular primal-dynamics solver for constrained optimization problems, including distributed time-varying problems in continuous time.
Pedro Cisneros-Velarde received the B.Sc. in Electrical Engineering at the Pontifical Catholic University of Peru (PUCP), Lima, Peru; an M.Sc. in Electrical Engineering, an M.A. in Statistics and a recent Ph.D. in Electrical Engineering at the University of California, Santa Barbara (UCSB), CA, USA. He is also affiliated to the Center for Control, Dynamical Systems, and Computation at UCSB. He has worked in a variety of interdisciplinary problems covering the areas of mathematical sociology, control theory and statistics. His current research interests include the areas of statistical machine learning, optimization, and multi-agent systems.
Faculty Host: Sanmi Koyejo