  Partially observable Markov Decision Processes (POMDPs) are a standard model
for agents making decisions in uncertain environments. Most work on POMDPs
focuses on synthesizing strategies based on the available capabilities.
However, system designers can often control an agent's observation
capabilities, e.g. by placing or selecting sensors. This raises the question of
how one should select an agent's sensors cost-effectively such that it achieves
the desired goals. In this paper, we study the novel optimal observability
problem OOP: Given a POMDP M, how should one change M's observation
capabilities within a fixed budget such that its (minimal) expected reward
remains below a given threshold? We show that the problem is undecidable in
general and decidable when considering positional strategies only. We present
two algorithms for a decidable fragment of the OOP: one based on optimal
strategies of M's underlying Markov decision process and one based on parameter
synthesis with SMT. We report promising results for variants of typical
examples from the POMDP literature.
