Many iterative algorithms are designed to solve challenging signal processing and machine learning optimization problems. Among such algorithms are iterative hard thresholding for sparse reconstruction, projected gradient descent for matrix completion, and alternating projection for phase retrieval. Such algorithms and others can be viewed through the fix-point iteration lens. In this talk, we will examine the fixed-point view of iterative algorithms. We will present results on the analysis of projected gradient descent for the well-known constrained least squares problem and show how such analysis can be used to optimize the iterative solution. As a special case of this framework, we will examine iterative solutions to the matrix completion problem. Our approach provides a stepping stone to the optimization of acceleration approaches across multiple algorithms.
Raviv Raich received the B.Sc. and M.Sc. degrees in electrical engineering from Tel-Aviv University, Tel-Aviv, Israel, in 1994 and 1998, respectively, and the Ph.D. degree in electrical engineering from the Georgia Institute of Technology, Atlanta, GA, in 2004. Between 1999 and 2000, he was a Researcher with the Communications Team, Industrial Research, Ltd., Wellington, New Zealand. From 2004 to 2007, he was a Postdoctoral Fellow with the University of Michigan, Ann Arbor, MI. Raich has been an assistant professor (2007-2013) and an associate professor (2013-2023) with the School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR. His research interests include probabilistic modeling and optimization in signal processing and machine learning. From 2011 to 2014, he was an Associate Editor for the IEEE Transactions on Signal Processing. He was a Member during 2011–2016 and the Chair during 2017–2018 of the Machine Learning for Signal Processing Technical Committee (TC) of the IEEE Signal Processing Society. Since 2019, he has been a Member of the Signal Processing Theory and Methods, TC of the IEEE Signal Processing Society.