On the Computational Complexity of Stochastic Controller Optimization in POMDPs

被引：40

作者：

Vlassis, Nikos ^{[1
]}

Littman, Michael L. ^{[2
]}

Barber, David ^{[3
]}

机构：

[1] Univ Luxembourg, Luxembourg Ctr Syst Biomed, 7 Ave Hauts Fourneaux, L-4362 Esch Belval, Luxembourg

[2] Brown Univ, Dept Comp Sci, Providence, RI 02912 USA

[3] UCL, Dept Comp Sci, London WC1E 6BT, England

来源：

ACM TRANSACTIONS ON COMPUTATION THEORY | 2012年 / 4卷 / 04期

基金：

美国国家科学基金会;

关键词：

Performance; Partially observable Markov decision process; stochastic controller; bilinear program; computational complexity; Motzkin-Straus theorem; sum-of-square-roots problem; matrix fractional program; computations on polynomials; nonlinear optimization;

D O I：

10.1145/2382559.2382563

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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.

引用

页数：8

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