基于线性分类器的决策树策略表示
Strategy Representation by Decision Trees with Linear Classifiers
摘要：
图博弈和马尔可夫决策过程（MDP）是不确定性概率系统反应式综合和验证的标准模型。$ω$类-常规获胜条件;例如，安全性，可达性，活性，奇偶校验条件;提供了一个强大的和表达规范形式主义的属性，出现在反应系统的分析。在游戏和MDPs的非决定性的决议表示为战略，我们认为这种战略的简洁表示。机器学习的决策树数据结构保留了策略决策的味道，并允许基于熵的最小化来获得简洁的树。然而，与允许小错误的传统机器学习问题相反，对于图游戏和MDP中的获胜策略，不允许错误，并且决策树必须代表整个策略。在这项工作中，我们提出了决策树与线性分类器表示的战略图游戏和MDPs。我们已经实现了使用这种数据结构的战略表示，我们提出的实验结果，图游戏和MDPs的问题，这表明，这种新的数据结构提出了一个更有效的战略表示相比，标准的决策树。
英文摘要：
Graph games and Markov decision processes (MDPs) are standard models in reactive synthesis and verification of probabilistic systems with nondeterminism. The class of $ω$-regular winning conditions; e.g., safety, reachability, liveness, parity conditions; provides a robust and expressive specification formalism for properties that arise in analysis of reactive systems. The resolutions of nondeterminism in games and MDPs are represented as strategies, and we consider succinct representation of such strategies. The decision-tree data structure from machine learning retains the flavor of decisions of strategies and allows entropy-based minimization to obtain succinct trees. However, in contrast to traditional machine-learning problems where small errors are allowed, for winning strategies in graph games and MDPs no error is allowed, and the decision tree must represent the entire strategy. In this work we propose decision trees with linear classifiers for representation of strategies in graph games and MDPs. We have implemented strategy representation using this data structure and we present experimental results for problems on graph games and MDPs, which show that this new data structure presents a much more efficient strategy representation as compared to standard decision trees.
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