- Series
- ACO Student Seminar
- Time
- Friday, March 6, 2020 - 1:05pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Aditi Laddha – CS, Georgia Tech – aladdha6@gatech.edu – https://www.cc.gatech.edu/~aladdha6/
- Organizer
- He Guo
Motivated by the Dikin walk, we develop aspects of an interior-point
theory for sampling in high dimensions. Specifically, we introduce symmetric
and strong self-concordance. These properties imply that the corresponding
Dikin walk mixes in steps from a warm start
in a convex body in using a strongly self-concordant barrier
with symmetric self-concordance parameter . For many natural
barriers, is roughly bounded by , the standard
self-concordance parameter. We show that this property and strong
self-concordance hold for the Lee-Sidford barrier. As a consequence,
we obtain the first walk to mix in steps for an
arbitrary polytope in . Strong self-concordance for other
barriers leads to an interesting (and unexpected) connection ---
for the universal and entropic barriers, it is implied by the KLS
conjecture.