On the Computational Complexity of Stochastic Controller Optimization in   POMDPs
  We show that the problem of finding an optimal stochastic 'blind' controller in a Markov decision process is an NP-hard problem. The corresponding decision problem is NP-hard, in PSPACE, and SQRT-SUM-hard, hence placing it in NP would imply breakthroughs in long-standing open problems in computer science. Our result establishes that the more general problem of stochastic controller optimization in POMDPs is also NP-hard. Nonetheless, we outline a special case that is convex and admits efficient global solutions. 
Nikos Vlassis, Michael L. Littman, David Barber
cs.CC cs.LG cs.SY math.OC