  We present an algorithm for formal verification and parameter synthesis of
continuous state-space Markov chains. This class of problems captures the
design and analysis of a wide variety of autonomous and cyber-physical systems
defined by nonlinear and black-box modules. In order to solve these problems,
one has to maximize certain probabilistic objective functions overall choices
of initial states and parameters. In this paper, we identify the assumptions
that make it possible to view this problem as a multi-armed bandit problem.
Based on this fresh perspective, we propose an algorithm (HOO-MB) for solving
the problem that carefully instantiates an existing bandit algorithm --
Hierarchical Optimistic Optimization -- with appropriate parameters. As a
consequence, we obtain theoretical regret bounds on sample efficiency of our
solution that depends on key problem parameters like smoothness,
near-optimality dimension, and batch size. The batch size parameter enables us
to strike a balance between the sample efficiency and the memory usage of the
algorithm. Our experiments, using the tool HooVer, suggest that the approach
scales to realistic-sized problems and is often more sample-efficient compared
to PlasmaLab -- a leading tool for verification of stochastic systems.
Specifically, HooVer has distinct advantages in analyzing models in which the
objective function has sharp slopes. In addition, HooVer shows promising
behavior in parameter synthesis for a linear quadratic regulator (LQR) example.
