On the Computational Complexity of Stochastic Controller Optimization in POMDPs

Abstract

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.