Veranstaltungen

07. September 2023, 15:59 bis 18:00

AKOR Seminar: Alternating minimization and some generalizations of convexity

Seminar

Pierre-Cyril Aubin, TU Wien

I will present my recent research in going beyond the quadratic cost in optimization, by replacing it with a general cost function. With Flavien Léger (INRIA Paris), we unveiled in arxiv.org/abs/2305.04917, öffnet eine externe URL in einem neuen Fenster a new class of gradient-type optimization methods that extends vanilla gradient descent, mirror descent, Riemannian gradient descent, and natural gradient descent. Our approach involves constructing a surrogate for the objective function in a systematic manner, based on a chosen cost function. This surrogate is then minimized using an alternating minimization scheme. Using optimal transport theory we establish convergence rates based on generalized notions of smoothness and convexity. We provide local versions of these two notions when the cost satisfies a condition known as nonnegative cross-curvature. In particular our framework provides the first global rates for natural gradient descent and Newton's method. For a quick read of arxiv.org/abs/2305.04917, öffnet eine externe URL in einem neuen Fenster I recommend reading the summary p4-6 and then look for your favorite algorithm (mirror, Riemannian, etc) in Section 4. 

Kalendereintrag

Veranstaltungsort

Sem. R. DB 04
1040 Wien

 

Veranstalter

VADOR
vador@tuwien.ac.at

 

Info-Link

https://arxiv.org/abs/2305.04917

 

Öffentlich

Nein

 

Kostenpflichtig

Nein

 

Anmeldung erforderlich

Nein