  We study the problem of policy synthesis for uncertain partially observable
Markov decision processes (uPOMDPs). The transition probability function of
uPOMDPs is only known to belong to a so-called uncertainty set, for instance in
the form of probability intervals. Such a model arises when, for example, an
agent operates under information limitation due to imperfect knowledge about
the accuracy of its sensors. The goal is to compute a policy for the agent that
is robust against all possible probability distributions within the uncertainty
set. In particular, we are interested in a policy that robustly ensures the
satisfaction of temporal logic and expected reward specifications. We state the
underlying optimization problem as a semi-infinite quadratically-constrained
quadratic program (QCQP), which has finitely many variables and infinitely many
constraints. Since QCQPs are non-convex in general and practically infeasible
to solve, we resort to the so-called convex-concave procedure to convexify the
QCQP. Even though convex, the resulting optimization problem still has
infinitely many constraints and is NP-hard. For uncertainty sets that form
convex polytopes, we provide a transformation of the problem to a convex QCQP
with finitely many constraints. We demonstrate the feasibility of our approach
by means of several case studies that highlight typical bottlenecks for our
problem. In particular, we show that we are able to solve benchmarks with
hundreds of thousands of states, hundreds of different observations, and we
investigate the effect of different levels of uncertainty in the models.
