On the Computational Complexity of Stochastic Controller Optimization in POMDPs
Computational Complexity
2012-10-05 v2 Machine Learning
Systems and Control
Optimization and Control
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.
Cite
@article{arxiv.1107.3090,
title = {On the Computational Complexity of Stochastic Controller Optimization in POMDPs},
author = {Nikos Vlassis and Michael L. Littman and David Barber},
journal= {arXiv preprint arXiv:1107.3090},
year = {2012}
}
Comments
Corrected error in the proof of Theorem 2, and revised Section 5