  This note re-visits the rolling-horizon control approach to the problem of a
Markov decision process (MDP) with infinite-horizon discounted expected reward
criterion. Distinguished from the classical value-iteration approach, we
develop an asynchronous on-line algorithm based on policy iteration integrated
with a multi-policy improvement method of policy switching. A sequence of
monotonically improving solutions to the forecast-horizon sub-MDP is generated
by updating the current solution only at the currently visited state, building
in effect a rolling-horizon control policy for the MDP over infinite horizon.
Feedbacks from "supervisors," if available, can be also incorporated while
updating. We focus on the convergence issue with a relation to the transition
structure of the MDP. Either a global convergence to an optimal
forecast-horizon policy or a local convergence to a "locally-optimal"
fixed-policy in a finite time is achieved by the algorithm depending on the
structure.
