On the computational complexity of stochastic controller optimization in POMDPs

Details On the computational complexity of stochastic controller optimization in POMDPs On the computational complexity of stochastic controller optimization in POMDPs

2011-07-15

arxiv.org/abs/1107.3090v1

Computer Science

Computational Complexity

Scientific paper

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 a breakthrough in long-standing open problems in computer science. Our optimization 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 solvable to arbitrary accuracy in polynomial time via semidefinite or second-order cone programming.

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