Strong self concordance and sampling

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.eduhttps://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 O~(nν¯) steps from a warm start

in a convex body in Rn using a strongly self-concordant barrier

with symmetric self-concordance parameter ν¯. For many natural

barriers, ν¯ is roughly bounded by ν, 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 O~(n2) steps for an

arbitrary polytope in Rn. 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.