My research lies at the intersection of optimization and distributed computing, and targets applications in machine learning and image processing. I design optimization methods for a wide range of platforms. This includes powerful cluster/cloud computing environments for machine learning and computer vision, in addition to resource limited integrated circuits and FPGAs for real-time signal processing. My research takes an integrative approach that jointly considers theory, algorithms, and hardware to build practical, high-performance systems. Before joining the faculty at Maryland, I completed my PhD in Mathematics at UCLA, and was a research scientist at Rice University and Stanford University. I have been the recipient of several awards, including a Sloan Fellowship and SIAM’s DiPrima Prize.
Here are some of my most recent projects. I believe in reproducible research, and I try to develop open-source tools to accompany my research when possible. For a full list of software and projects, see my complete research page.
A number of non-convex optimization problems can be convexified by “lifting” strategies. These methods yield convex formulations at the cost of substantially increased dimensionality. PhaseMax is a new type of convex relaxation that does not require lifting; it solves problems in their original low-dimensional parameter space.
Classical machine learning methods, include stochastic gradient descent (aka backprop), work great on one machine, but don’t scale well to the cloud or cluster setting. We propose a variety of algorithmic frameworks for scaling machine learning across many workers.
FASTA (Fast Adaptive Shrinkage/ Thresholding Algorithm) is an efficient, easy-to-use implementation of the Forward-Backward Splitting (FBS) method (also known as the proximal gradient method) for regularized optimization problems. Many variations on FBS are available in FASTA, including the popular accelerated variant FISTA (Beck and Teboulle ’09), the adaptive stepsize rule SpaRSA
PDHG is a powerful splitting method that can solve a wide range of constrained and non-differentiable optimization problems. Unlike the popular ADMM method, the PDHG approach usually does not require expensive minimization sub-steps. We provide adaptive stepsize selection rules that automate the solver, while increasing its speed and robustness.
My research is made possible by the generous support of the following organizations.
