Session III.3 - Computational Optimal Transport
Poster
Gradient descent with a general cost
Pierre-Cyril Aubin
INRIA SIERRA, France - This email address is being protected from spambots. You need JavaScript enabled to view it.
How to design algorithms that extend classical methods (and their convergence theory) beyond the Euclidean setting? How to integrate different families of algorithms into a unified framework? How to systematically approximate optimization problems? We show that c-transforms allow to build majorizing surrogates, which can be tackled through alternating minimization. The ``five-point property'' of Csiszar and Tusnady gives (sub)linear convergence rates for the values of the iterates. This property corresponds to a novel notion of c-semiconvexity, extending relative strong convexity, and intimately related to the MTW tensor . The mirror/Riemannian/natural gradient descent algorithms can all be cast in this formalism, leading to novel convergence conditions and rates.
Joint work with Flavien Léger (INRIA MOKAPLAN, France).