Next week, on June 7, at 4pm, Michael will give a seminar at INRIA, rue du Charolais, Paris 12 (map). Here is the abstract:
A Variational Perspective on Accelerated Methods in Optimization
Accelerated gradient methods play a central role in optimization,achieving optimal rates in many settings. While many generalizations and extensions of Nesterov’s original acceleration method have been proposed,it is not yet clear what is the natural scope of the acceleration concept.In this paper, we study accelerated methods from a continuous-time perspective. We show that there is a Lagrangian functional that we call the Bregman Lagrangian which generates a large class of accelerated methods in continuous time, including (but not limited to) accelerated gradient descent, its non-Euclidean extension, and accelerated higher-order gradient methods. We show that the continuous-time limit of all of these methods correspond to travelling the same curve in space time at different speeds, and in this sense the continuous-time setting is the natural one for understanding acceleration. Moreover, from this perspective, Nesterov’s technique and many of its generalizations can be viewed as a systematic way to go from the continuous-time curves generated by the Bregman Lagrangian to a family of discrete-time accelerated algorithms. [Joint work with Andre Wibisono and Ashia Wilson.]
(Interested readers need to register to attend the lecture.)
