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SUMMARY:Variational Principles for Mirror Descent and Mirror Langevin Dyna
 mics - Belinda Tzen (Columbia University)
DTSTART:20240718T123000Z
DTEND:20240718T133000Z
UID:TALK219058@talks.cam.ac.uk
DESCRIPTION:Mirror descent is a primal-dual convex optimization method tha
 t can be tailored to the geometry of the optimization problem at hand thro
 ugh the choice of a strongly convex potential function. It arises as a bas
 ic primitive in a variety of applications\, including large-scale optimiza
 tion\, machine learning\, and control. We propose a variational formulatio
 n of mirror descent and of its most straightforward stochastic analogue\, 
 mirror Langevin dynamics. The main idea leverages variational principles f
 or gradient flows to show that (1) mirror descent emerges as a closed-loop
  solution for a certain optimal control problem\; and (2) the Bellman valu
 e function is given by the Bregman divergence between the initial conditio
 n and the global minimizer of the objective function.
LOCATION:External
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