[Theory] [Theory Lunch] Ali Vakilian, Wednesday, 10/9 12-1pm, JCL 390

[Gabe Schoenbach via Theory]

Hi all — please join us this *Wednesday at 12pm* for theory lunch! (Note
the half-hour earlier start time this year). Details below:

*****
*Date: *October 9, 2024
*Time: *12:00pm
*Location: *JCL 390

*Title: *Tight Bounds for Volumetric Spanners and Applications

*Speaker: *Ali Vakilian, TTIC

*Abstract:* Given a set of points of interest, a volumetric spanner is a
subset of the points using which all the points can be expressed using
"small" coefficients (measured in an appropriate norm). Formally, given a
set of vectors $X = \{v_1, v_2, \dots, v_n\}$, the goal is to find $T
\subseteq [n]$ such that every $v \in X$ can be expressed as $\sum_{i\in T}
\alpha_i v_i$, with $||\alpha||$ being small.  This notion, which has also
been referred to as a well-conditioned basis, has found several
applications, including bandit linear optimization, determinant
maximization, and matrix low rank approximation. In this paper, we give
almost optimal bounds on the size of volumetric spanners for all $\ell_p$
norms, and show that they can be constructed using a simple local search
procedure. We then show the applications of our result to other tasks and
in particular the problem of finding coresets for the Minimum Volume
Enclosing Ellipsoid (MVEE) problem.

Joint work with Aditya Bhaskara (University of Utah) and Sepideh Mahabadi
(Microsoft Research--Redmond).
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