Seminar Details
2021-11-16 (14h) : Gradient methods with Bregman distances
At Euler building (room a.002)
Organized by Mathematical Engineering
Speaker :
Radu Dragomir (UCL/INMA)
Abstract :
Large-scale optimization problems from signal processing and machine learning are typically solved with gradient methods, because of their low cost per iteration and their simplicity. In this talk, we study a generalization of the standard gradient descent, which consists in replacing the Euclidean distance by a more general Bregman divergence induced by some simple convex reference function. This function is chosen to be adapted to the geometry of the problem at hand through the so-called relative smoothness condition.
We present some advances in this recent line of work, including the study of worst-case complexity through performance estimation problems (PEPs), as well as applications to low-rank matrix optimization.