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Compositional reasoning for weighted Markov decision processes

机译：加权马尔可夫决策过程的成分推理

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Weighted Markov decision processes (MDPs) have long been used to model quantitative aspects of systems in the presence of uncertainty. However, much of the literature on such MDPs takes a monolithic approach, by modelling a system as a particular MDP; properties of the system are then inferred by analysis of that particular MDP. In contrast in this paper we develop compositional methods for reasoning about weighted MDPs, as a possible basis for compositional reasoning about their quantitative behaviour. In particular we approach these systems from a process algebraic point of view. For these we define a coinductive simulation-based behavioural preorder which is compositional in the sense that it is preserved by structural operators for constructing weighted MDPs from components. For finitary convergent processes, which are finite-state and finitely branching systems without divergence, we provide two characterisations of the behavioural preorder. The first uses a novel quantitative probabilistic logic, while the second is in terms of a novel form of testing, in which benefits are accrued during the execution of tests.
机译：加权马尔可夫决策过程（MDP）长期以来一直用于在存在不确定性的情况下对系统的定量方面进行建模。但是，有关此类MDP的许多文献都采用整体方法，将系统建模为特定的MDP。然后，通过对该特定MDP的分析来推断系统的属性。相反，在本文中，我们开发了用于加权MDP推理的组合方法，作为对其定量行为进行组合推理的可能基础。特别是，我们从过程代数的角度来研究这些系统。为此，我们定义了一个基于协演模拟的行为预购，该预购在结构上被结构算子保留下来，以便从组件中构造加权的MDP，因此具有一定的组成性。对于最终的收敛过程，它们是没有散度的有限状态和有限分支系统，我们提供了行为前序的两个特征。第一种使用新颖的定量概率逻辑，而第二种则采用新颖的测试形式，在执行测试过程中会产生收益。

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