Nonapproximability Results for Partially Observable Markov Decision Processes

We show that for several variations of partially observable Markov decision processes, polynomial-time algorithms for nding control policies are unlikely to or simply don't have guarantees of nding policies within a constant factor or a constant summand of optimal. Here \unlikely" means \unless some complexity classes collapse," where the collapses considered are P = NP, P = PSPACE, or P = EXP. Until or unless these collapses are shown to hold, any control-policy designer must choose between such performance guarantees and eecient computation.