Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A distance for probability spaces, and long-term values in Markov
  Decision Processes and Repeated Games   Given a finite set $K$, we denote by $X=\Delta(K)$ the set of probabilities
on $K$ and by $Z=\Delta_f(X)$ the set of Borel probabilities on $X$ with finite
support. Studying a Markov Decision Process with partial information on $K$
naturally leads to a Markov Decision Process with full information on $X$. We
introduce a new metric $d_*$ on $Z$ such that the transitions become
1-Lipschitz from $(X, \|.\|_1)$ to $(Z,d_*)$. In the first part of the article,
we define and prove several properties of the metric $d_*$. Especially, $d_*$
satisfies a Kantorovich-Rubinstein type duality formula and can be
characterized by using disintegrations. In the second part, we characterize the
limit values in several classes of "compact non expansive" Markov Decision
Processes. In particular we use the metric $d_*$ to characterize the limit
value in Partial Observation MDP with finitely many states and in Repeated
Games with an informed controller with finite sets of states and actions.
Moreover in each case we can prove the existence of a generalized notion of
uniform value where we consider not only the Ces\`aro mean when the number of
stages is large enough but any evaluation function $\theta \in \Delta(\N^*)$
when the impatience $I(\theta)=\sum_{t\geq 1} |\theta_{t+1}-\theta_t|$ is small
enough.

28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat