Title: Computational Techniques for Nonlinear Machine Learning Problems
Abstract: Nonlinearity appears in many areas of machine learning (ML), such as deep learning, reinforcement learning, graphical models, and adversarial ML. Given the large-scale nature and complexity of ML problems, nonlinearity has often been handled by heuristic techniques. These methods are behind the major successes of artificial intelligence in the past five years, but they lack mathematical guarantees. This has limited the applications of these methods to safety-critical systems, such as power systems and transportation systems. In this talk, we develop a set of computational tools with mathematical guarantees for various nonlinear problems in ML. First, we work through the notions of restricted isometry property, Kernel structure property and spurious solutions to understand when the best (global) solution of a nonlinear learning or optimization problem can be found via local search techniques. We demonstrate the results on the state estimation problem for power systems and show how much data should be collected to break down the complexity of the underlying learning problem in power systems. We then study the problem of learning a model under adversarial attacks on the data using the notion of graphical mutual incoherence, and as an example we use our results to design the first vulnerability map of the U.S. power grid. We also study the nonlinearity in reinforcement learning, where an infinite-dimensional control policy should be learned via interactions with an uncertain environment. We introduce the notion of spurious control policy to study when the true control policy can be efficiently learned.
Biography: Javad Lavaei is an Associate Professor in the Department of Industrial Engineering and Operations Research at UC Berkeley. His research spans optimization theory, control theory, machine learning, and power systems. He is a senior editor of the IEEE Systems Journal and has served as an associate editor for IEEE Transactions on Smart Grid, IEEE Transactions on Automatic Control, IEEE Transactions on Control of Network Systems, and IEEE Control Systems Letters. He has won several awards, including DARPA Young Faculty Award, DARPA Director's Fellowship, ONR Young Investigator Award, ONR Director of Research Early Career Grant, AFOSR Young Investigator Award, NSF CAREER Award, Google Faculty Research Award, INFORMS Optimization Society Prize for Young Researchers, Best Journal Paper Award of the IEEE Power & Energy Society, Donald P. Eckman Award of the American Automatic Control Council, INFORMS Energy Best Publication Award, SIAM Control and Systems Theory Prize, and 6 best conference paper awards. He has also received the Presidential Early Career Award for Scientists and Engineers.