Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularized unbalanced optimal transport as entropy minimization with
  respect to branching Brownian motion   We consider the problem of minimizing the entropy of a law with respect to
the law of a reference branching Brownian motion under density constraints at
an initial and final time. We call this problem the branching Schr\"odinger
problem by analogy with the Schr\"odinger problem, where the reference process
is a Brownian motion. Whereas the Schr\"odinger problem is related to
regularized (a.k.a. entropic) optimal transport, we investigate here the link
of the branching Schr\"odinger problem with regularized unbalanced optimal
transport.
  This link is shown at two levels. First, relying on duality arguments, the
values of these two problems of calculus of variations are linked, in the sense
that the value of the regularized unbalanced optimal transport (seen as a
function of the initial and final measure) is the lower semi-continuous
relaxation of the value of the branching Schr\"odinger problem. Second, we also
explicit a correspondence between the competitors of these two problems, and to
that end we provide a fine description of laws having a finite entropy with
respect to a reference branching Brownian motion.
  We investigate the small noise limit, when the noise intensity of the
branching Brownian motion goes to $0$: in this case we show, at the level of
the optimal transport model, that there is convergence to partial optimal
transport. We also provide formal arguments about why looking at the branching
Brownian motion, and not at other measure-valued branching Markov processes,
like superprocesses, yields the problem closest to optimal transport. Finally,
we explain how this problem can be solved numerically: the dynamical
formulation of regularized unbalanced optimal transport can be discretized and
solved via convex optimization.

5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: physics
31
The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: bayes-an