Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal measures and Markov transition kernels   We study optimal solutions to an abstract optimization problem for measures,
which is a generalization of classical variational problems in information
theory and statistical physics. In the classical problems, information and
relative entropy are defined using the Kullback-Leibler divergence, and for
this reason optimal measures belong to a one-parameter exponential family.
Measures within such a family have the property of mutual absolute continuity.
Here we show that this property characterizes other families of optimal
positive measures if a functional representing information has a strictly
convex dual. Mutual absolute continuity of optimal probability measures allows
us to strictly separate deterministic and non-deterministic Markov transition
kernels, which play an important role in theories of decisions, estimation,
control, communication and computation. We show that deterministic transitions
are strictly sub-optimal, unless information resource with a strictly convex
dual is unconstrained. For illustration, we construct an example where, unlike
non-deterministic, any deterministic kernel either has negatively infinite
expected utility (unbounded expected error) or communicates infinite
information.

17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess