Dan Garber - CS-Lecture -
Monday, 28.11.2016, 10:30
Projected gradient descent (PGD), and its close variants, are often
considered the methods of choice for solving a large variety of machine
learning optimization problems, including empirical risk minimization,
statistical learning, and online learning. This is not surprising, since
PGD is often optimal in a very appealing information-theoretic sense.
However, for many problems PGD is infeasible both in theory and practice
since each step requires to compute an orthogonal projection onto the
feasible set. In many important cases, such as when the feasible set is
a non-trivial polytope, or a convex surrogate for a low-rank structure,
computing the projection is computationally inefficient in
high-dimensional settings. An alternative is the conditional gradient
method (CG), aka Frank-Wolfe algorithm, that replaces the expensive
projection step with a linear optimization step over the feasible set.
Indeed in many problems of interest, the linear optimization step admits
much more efficient algorithms than the projection step, which is the
reason to the substantial regained interest in this method in the past
decade. On the downside, the convergence rates of the CG method often
fall behind that of PGD and its variants.
In this talk I will survey an ongoing effort to design CG variants that
on one hand enjoy the cheap iteration complexity of the original method,
and on the other hand converge provably faster, and are applicable to a
wider variety of machine learning settings. In particular I will focus
on the cases in which the feasible set is either a polytope or a convex
surrogate for low-rank matrices. Results will be demonstrated on
applications including: LASSO, video co-localization, optical character
recognition, matrix completion, and multi-class classification.
Dan's research interests lie in the intersection of machine learning and
continuous optimization. Dan's main focus is on the development of
efficient algorithms with novel and provable performance guarantees for
machine learning, data analysis, decision making and optimization
Dan is currently a Research Assistant Professor at Toyota Technological
Institute at Chicago, a philanthropically endowed academic computer
science institute located on the University of Chicago campus.
Previously, he received both his Ph.D and his M.Sc degrees from the
Technion - Israel Institute of Technology, where he worked under the
supervision of Prof. Elad Hazan. Before that, Dan completed his
bachelor's degree in electrical engineering, also in the Technion.