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SUMMARY:On the Relation between Optimal Transport and Schroedinger Bridges
 : A Control Perspective - Michele Pavon\, University of Padova
DTSTART:20150901T100000Z
DTEND:20150901T110000Z
UID:TALK60538@talks.cam.ac.uk
CONTACT:Tim Hughes
DESCRIPTION:We take a new look at the relation between the optimal transpo
 rt problem and the Schroedinger bridge problem from a control perspective.
  Our aim is to highlight new connections between the two that are richer a
 nd deeper than those previously described in the literature. We begin with
  an elementary derivation of the Benamou-Brenier fluid dynamic version of 
 the optimal transport problem and provide\, in parallel\, a new fluid dyna
 mic version of the Schroedinger bridge problem. We observe that the latter
  establishes an important connection with optimal transport without zero-n
 oise limits and solves a question posed by Eric Carlen in 2006.  Indeed\, 
  the two variational problems differ by a Fisher information functional.\n
 \nWe then consider a generalization of optimal mass transport in the form 
 of a (fluid dynamic) problem of optimal transport with prior. This can be 
 seen as the zero-noise limit of Schroedinger bridges when the prior is any
  Markovian evolution. We finally specialize to the Gaussian case and deriv
 e an explicit computational theory based on matrix Riccati differential  e
 quations. 
LOCATION:Cambridge University Engineering Department\, LR5
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