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CATEGORIES:CUED Control Group Seminars
SUMMARY:On the Relation between Optimal Transport and Schr
oedinger Bridges: A Control Perspective - Michele
Pavon\, University of Padova
DTSTART;TZID=Europe/London:20150901T110000
DTEND;TZID=Europe/London:20150901T120000
UID:TALK60538AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/60538
DESCRIPTION:We take a new look at the relation between the opt
imal transport problem and the Schroedinger bridge
problem from a control perspective. Our aim is to
highlight new connections between the two that ar
e richer and deeper than those previously describe
d in the literature. We begin with an elementary d
erivation of the Benamou-Brenier fluid dynamic ver
sion of the optimal transport problem and provide\
, in parallel\, a new fluid dynamic version of the
Schroedinger bridge problem. We observe that the
latter establishes an important connection with op
timal transport without zero-noise limits and solv
es a question posed by Eric Carlen in 2006. Indee
d\, the two variational problems differ by a Fish
er information functional.\n\nWe then consider a g
eneralization of optimal mass transport in the for
m of a (fluid dynamic) problem of optimal transpor
t with prior. This can be seen as the zero-noise l
imit of Schroedinger bridges when the prior is any
Markovian evolution. We finally specialize to the
Gaussian case and derive an explicit computationa
l theory based on matrix Riccati differential equ
ations.
LOCATION:Cambridge University Engineering Department\, LR5
CONTACT:Tim Hughes
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