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arXiv 1111.0062cs.AI
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分散POMDPs的最优和近似Q-价值函数

Optimal and Approximate Q-value Functions for Decentralized POMDPs

University of Amsterdam(阿姆斯特丹大学);Instituto Superior Técnico(里斯本高等理工学院);Technical University of Crete(克里特理工大学)

Frans A. Oliehoek, Matthijs T. J. Spaan, Nikos Vlassis

摘要:

决策理论规划是一种流行的方法,顺序决策问题,因为它处理的不确定性,在传感器和行动的原则。在MDP和POMDP等单智能体框架中,规划可以通过求助于Q-价值函数来执行:通过动态规划以递归方式计算最优Q-值函数Q*,然后从Q* 中提取最优策略。在本文中,我们研究是否可以定义类似的Q-价值函数的分散POMDP模型(Dec-POMDP),以及如何从这样的价值函数中提取政策。我们定义了两种形式的最佳Q-价值函数的Dec-POMDPs:一个是一个规范的描述作为Q-价值函数的最佳纯联合政策和另一个是顺序合理的,从而给出了一个配方的计算。然而,除了最小的问题之外,这种计算对所有问题都是不可行的。因此,我们分析了各种近似Q-价值函数,允许有效的计算。我们描述了它们之间的关系,并证明了它们都提供了最优Q-价值函数Q* 的上界。最后,统一以前的一些方法来解决Dec-POMDPs,我们描述了一个家庭的算法,从这样的Q-价值函数提取政策,并进行实验评估现有的测试问题,包括一个新的消防基准问题。

英文摘要:

Decision-theoretic planning is a popular approach to sequential decision making problems, because it treats uncertainty in sensing and acting in a principled way. In single-agent frameworks like MDPs and POMDPs, planning can be carried out by resorting to Q-value functions: an optimal Q-value function Q* is computed in a recursive manner by dynamic programming, and then an optimal policy is extracted from Q*. In this paper we study whether similar Q-value functions can be defined for decentralized POMDP models (Dec-POMDPs), and how policies can be extracted from such value functions. We define two forms of the optimal Q-value function for Dec-POMDPs: one that gives a normative description as the Q-value function of an optimal pure joint policy and another one that is sequentially rational and thus gives a recipe for computation. This computation, however, is infeasible for all but the smallest problems. Therefore, we analyze various approximate Q-value functions that allow for efficient computation. We describe how they relate, and we prove that they all provide an upper bound to the optimal Q-value function Q*. Finally, unifying some previous approaches for solving Dec-POMDPs, we describe a family of algorithms for extracting policies from such Q-value functions, and perform an experimental evaluation on existing test problems, including a new firefighting benchmark problem.

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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