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Statistics Seminar - "On the analysis of Bregman-surrogate algorithms for nonsmooth nonconvex optimization" - Dr. Yiyuan She - Florida State University

Event Type
Xiaohui Chen
Oct 19, 2017   3:30 pm  

Title: On the analysis of Bregman-surrogate algorithms for nonsmooth
nonconvex optimization

Abstract: Modern statistical problems often involve minimizing objective functions
that are not necessarily convex or smooth. This paper investigates a
broad surrogate framework defined by generalized Bregman divergence
functions for developing scalable algorithms. Local linear
approximation, mirror descent, iterative thresholding, and DC
programming can all be viewed as particular instances. The Bregman
re-characterization enables us to choose suitable measures of
computational error to establish global convergence rate results even
for nonconvex problems in high-dimensional settings. Moreover, under
some regularity conditions, the sequence of iterates in Bregman
surrogate optimization can be shown to approach the statistical truth
within the desired accuracy geometrically fast. The algorithms can be
accelerated with a careful control of relaxation and stepsize
parameters. Simulation studies are performed to support the theoretical
results. This is joint work with Zhifeng Wang.

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