部分可观测马尔可夫决策过程的定性分析
Qualitative Analysis of Partially-observable Markov Decision Processes
摘要：
我们研究了部分可观测马尔可夫决策过程（POMDPs）与欧米茄定期目标的观察为基础的战略。基于观察的策略依赖于关于游戏历史的部分信息，即过去的观察序列。我们考虑的定性分析问题：给定一个POMDP与一个欧米伽正则目标，是否有一个基于观察的策略，以达到目标的概率约1（几乎肯定获胜），或与积极的概率（积极获胜）。我们的主要结果是双重的。首先，我们提出了一个完整的图片的计算复杂性的定性分析POMDP的奇偶性目标（一个规范形式来表达ω-经常目标）及其子类。我们的贡献在于建立了几个在文献中不为人知的上限和下限。其次，我们提出了最佳的界限（匹配的上限和下限）的内存所需的纯随机观察为基础的策略，POMDP的奇偶校验目标及其子类的定性分析。
英文摘要：
We study observation-based strategies for partially-observable Markov decision processes (POMDPs) with omega-regular objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past sequence of observations. We consider the qualitative analysis problem: given a POMDP with an omega-regular objective, whether there is an observation-based strategy to achieve the objective with probability~1 (almost-sure winning), or with positive probability (positive winning). Our main results are twofold. First, we present a complete picture of the computational complexity of the qualitative analysis of POMDP s with parity objectives (a canonical form to express omega-regular objectives) and its subclasses. Our contribution consists in establishing several upper and lower bounds that were not known in literature. Second, we present optimal bounds (matching upper and lower bounds) on the memory required by pure and randomized observation-based strategies for the qualitative analysis of POMDP s with parity objectives and its subclasses.
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