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arXiv 1301.3836cs.AI
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马氏决策过程分散控制的复杂性

The Complexity of Decentralized Control of Markov Decision Processes

University of Massachusetts Amherst(马萨诸塞大学阿默斯特分校)

Daniel S Bernstein, Shlomo Zilberstein, Neil Immerman

摘要:

从决策论的角度考虑了具有部分状态信息的分布式智能体的规划问题.我们描述了广义的MDP和POMDP模型,允许分散控制。即使是少量的代理人,我们的两个模型对应的有限时域问题是完整的非确定性指数时间。这些复杂性的结果说明了马尔可夫过程的集中控制和分散控制之间的根本区别。与MDP和POMDP问题相比,我们考虑的问题可证明不允许多项式时间算法,并且在最坏的情况下很可能需要双指数时间来解决。因此,我们提供了相应的数学证据的直觉,分散的规划问题不能很容易地减少到集中的问题,并解决了使用既定的技术。

英文摘要:

Planning for distributed agents with partial state information is considered from a decision- theoretic perspective. We describe generalizations of both the MDP and POMDP models that allow for decentralized control. For even a small number of agents, the finite-horizon problems corresponding to both of our models are complete for nondeterministic exponential time. These complexity results illustrate a fundamental difference between centralized and decentralized control of Markov processes. In contrast to the MDP and POMDP problems, the problems we consider provably do not admit polynomial-time algorithms and most likely require doubly exponential time to solve in the worst case. We have thus provided mathematical evidence corresponding to the intuition that decentralized planning problems cannot easily be reduced to centralized problems and solved exactly using established techniques.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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