Planning with Delayed State Information

We consider a special case of partially observable Markov decision processes that arises when state information is perfect but arrives with a delay. We rst formulate the decision process in its standard form and derive the Bellman equation that corresponds to it. We then introduce a second decision process that has a much simpler Bellman equation than the rst, and is therefore, in general, much easier to solve. We demonstrate that even though the two decision processes have diierent optimal value functions, their optimal policies are the same. Exploitation of this result may lead to vast computational savings.