Pedro Domingos; Recursive Decomposition for Nonconvex Optimization

CORE Series
Tuesday, November 24, 2015, 4:00 pm
Gowen Hall, Room 201
Pedro Domingos,University of Washington.
Recursive Decomposition for Nonconvex Optimization

ABSTRACT: Most real-world continuous optimization problems are nonconvex, causing standard convex techniques to find only local optima, even with extensions like random restarts and simulated annealing. We observe that, in many cases, the local modes of the objective function have combinatorial structure, and thus ideas from combinatorial optimization can be brought to bear. Based on this, we propose a problem-decomposition approach to nonconvex optimization. Similarly to DPLL-style SAT solvers and recursive conditioning in probabilistic inference, our algorithm, RDIS, recursively sets variables so as to simplify and decompose the objective function into approximately independent subfunctions, until the remaining functions are simple enough to be optimized by standard techniques like gradient descent. The variables to set are chosen by graph partitioning, ensuring decomposition whenever possible. We show analytically that RDIS can solve a broad class of nonconvex optimization problems exponentially faster than gradient descent with random restarts. Experimentally, RDIS outperforms standard techniques on problems like structure from motion and protein folding.

Bio: Pedro Domingos is a professor of computer science at the University of Washington and the author of “The Master Algorithm”. He is a winner of the SIGKDD Innovation Award, the highest honor in data science. He is a Fellow of the Association for the Advancement of Artificial Intelligence, and has received a Fulbright Scholarship, a Sloan Fellowship, the National Science Foundation’s CAREER Award, and numerous best paper awards. He received his Ph.D. from the University of California at Irvine and is the author or co-author of over 200 technical publications. He has held visiting positions at Stanford, Carnegie Mellon, and MIT. He co-founded the International Machine Learning Society in 2001. His research spans a wide variety of topics in machine learning, artificial intelligence, and data science, including scaling learning algorithms to big data, maximizing word of mouth in social networks, unifying logic and probability, and deep learning.