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SUMMARY:Variational\, Hamiltonian and Symplectic Perspectives on Accelerat
 ion - Michael Jordan (University of California\, Berkeley)
DTSTART:20170704T080000Z
DTEND:20170704T084500Z
UID:TALK73138@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Accelerated gradient methods play a central role in optimizati
 on\, achieving optimal rates in many settings. &nbsp\;While many generaliz
 ations and extensions of Nesterov&#39\;s original acceleration method have
  been proposed\, it is not yet clear what is the natural scope of the acce
 leration<br>concept. We study accelerated methods from a continuous-time p
 erspective. &nbsp\;We show that there is a Lagrangian functional that we c
 all the "Bregman Lagrangian" which generates a large class of accelerated 
 methods in continuous time\, including (but not limited to) accelerated<br
 >gradient descent\, its non-Euclidean extension\, and accelerated higher-o
 rder gradient methods. &nbsp\;We show that the continuous-time limit of al
 l of these methods correspond to traveling the same curve in spacetime at 
 different speeds. &nbsp\;We also describe a "Bregman Hamiltonian" which ge
 nerates the accelerated dynamics\, we develop a symplectic integrator for 
 this Hamiltonian and we discuss relations between this symplectic integrat
 or and classical Nesterov acceleration. &nbsp\;[Joint work with Andre Wibi
 sono\, Ashia Wilson and Michael Betancourt.]<br>
LOCATION:Seminar Room 1\, Newton Institute
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