On the Computational Complexity of Stochastic Controller Optimization in POMDPs

Nikos Vlassis; Michael L. Littman; David Barber

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arXiv · 1107.3090

On the Computational Complexity of Stochastic Controller Optimization in POMDPs

Nikos Vlassis·Michael L. Littman·David Barber

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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.

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BibTeX RIS

Nikos Vlassis, Michael L. Littman, David Barber. 2011-07-15. On the Computational Complexity of Stochastic Controller Optimization in POMDPs. https://arxiv.org/abs/1107.3090

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