  This paper investigates MDPs with intermittent state information. We consider
a scenario where the controller perceives the state information of the process
via an unreliable communication channel. The transmissions of state information
over the whole time horizon are modeled as a Bernoulli lossy process. Hence,
the problem is finding an optimal policy for selecting actions in the presence
of state information losses. We first formulate the problem as a belief MDP to
establish structural results. The effect of state information losses on the
expected total discounted reward is studied systematically. Then, we
reformulate the problem as a tree MDP whose state space is organized in a tree
structure. Two finite-state approximations to the tree MDP are developed to
find near-optimal policies efficiently. Finally, we put forth a nested value
iteration algorithm for the finite-state approximations, which is proved to be
faster than standard value iteration. Numerical results demonstrate the
effectiveness of our methods.
